At the start of Harry Potter and the Sorcerer's/Philosopher's Stone, we see a day in the life of Vernon Dursley. At one point, Vernon accidentally bumps into a short wizard who is ecstatic about Voldemort's disappearance. Was this wizard Professor Flitwick?
Since Harry's parents were killed on Halloween, Hogwarts would be in-session, so Flitwick is likely there since he was a professor at the time. Even if he did leave the school to celebrate (Or was not at the school for some unmentioned reason due to the wizarding war going on), unlike Dumbledore, McGonagall, and Hagrid, Flitwick had no reason to come anywhere near the Dursleys.
Instead, I've always thought it was Dedalus Diggle. He has a similar physical description to Flitwick and he always wears shades of purple like the man that Vernon meets. He also is described as irresponsible which would match with the person Vernon meets who totally breaks the International Statute of Secrecy.
He also lives near Harry (So it makes sense he would run into Vernon as the celebrations started getting underway):
Yet sometimes he thought (or maybe hoped) that strangers in the street seemed to know him. A tiny man in a violet top hat had bowed to him once while out shopping with Aunt Petunia and Dudley.
Philosopher’s Stone - Chapter 2: The Vanishing Glass
This is confirmed to be Digggle later when Harry enters the Leaky Cauldron and is meeting all of the patrons:
A little man in a top hat was talking to the old bartender,
“Delighted, Mr. Potter, just can’t tell you, Diggle’s the name, Dedalus Diggle.”
“I’ve seen you before!” said Harry, as Dedalus Diggle’s top hat fell off in his excitement. “You bowed to me once in a shop.”
“He remembers!” cried Dedalus Diggle, looking around at everyone. “Did you hear that? He remembers me!”
Philosopher’s Stone - Chapter 5: Diagon Alley
And when the Advance Guard comes to take Harry to Grimmauld Place, his voice is squeaky:
"We've met before," squeaked the excitable Diggle, dropping his violet-coloured top hat.
Order of the Phoenix - Chapter 3: The Advance Guard
His voice is also described as squeaky in the Deathly Hallows:
“Harry Potter!” squeaked an excited voice, the moment Harry had opened the door; a small man in a mauve top hat was sweeping him a deep bow, “An honor, as ever!”
Deathly Hallows - Chapter 3: The Dursleys Departing
Lastly, he seems more likely to directly address Vernon and call him a Muggle than Flitwick does, since he is much more excitable than Flitwick. On the night Voldemort is defeated, McGonagall says that he is probably responsible for creating shooting stars which were picked up by Muggle news:
"Shooting stars down in Kent--I'll bet that was Dedalus Diggle. He never had much sense."
Philosopher's Stone - Chapter 1: The Boy Who Lived
It's unlikely that wizard was Flitwick.
Flitwick is unlikely to be roaming around the Dursleys' neighborhood. He'd either be at Hogwarts teaching, or helping in the war against Voldemort.
The wizard who excitedly tells Vernon about You-Know-Who disappearing and called him a Muggle wasn't being very cautious; wizards aren't supposed to tell Muggles about wizarding events or call them Muggles. Conversely, Flitwick seems very intelligent - he was the head of Ravenclaw House and he helped a lot in defending Hogwarts.
It's more likely, but nowhere near certain, that he was Dedalus Diggle.
The wizard's temperament matches Diggle far more than Flitwick. However, the only real evidence that he might be Diggle is that Diggle is also small and has a squeaky voice, and is known to have no sense and a liking for purple clothes.
He could have also been a different small wizard with a squeaky voice.
While "tiny and squeaky-voiced" does describe both Flitwick and Diggle, they probably aren't the only wizards who'd fit that description. Peter Pettigrew is also described as having a squeaky voice, and is also described as being very short, though not quite as short as Flitwick.
Diggle does in fact meet the Dursleys when the Order transports them to safety. Vernon is forced to interact with Diggle for quite a bit because of this, but neither of them gives any indication they've run into each other before.
“Good day to you, Harry Potter’s relatives!’ said Dedalus happily, striding into the living room. The Dursleys did not look at all happy to be addressed thus; Harry half expected another change of mind. Dudley shrank nearer to his mother at the sight of the witch and wizard.” - Harry Potter and the Deathly Hallows, Chapter 3 (The Dursleys Departing)
This supports that the man who ran into Vernon is probably not Diggle - such an odd man like Diggle would surely be memorable to the straight-laced Vernon, and Dedalus Diggle might also recognize Vernon as the same large and cranky Muggle.
So it can't be said for certain from the information given that this tiny wizard in a purple hat is one we see anywhere else. His fondness for purple, in itself, proves almost nothing. Purple is a fairly common color among wizards. Dumbledore wears purple quite a few times. He wore it the day he went to leave Harry at the Dursleys'.
“He was tall, thin and very old, judging by the silver of his hair and beard, which were both long enough to tuck into his belt. He was wearing long robes, a purple cloak which swept the ground and high-heeled, buckled boots.” - Harry Potter and the Philosopher's Stone
He wore purple to the feast at the start of the Hogwarts year.
“They lit first upon Professor Dumbledore, sitting in his high-backed golden chair at the centre of the long staff table, wearing deep-purple robes scattered with silvery stars and a matching hat.” - Harry Potter and the Order of the Phoenix
There are a few more times Dumbledore is mentioned as wearing purple as well - it's not an uncommon color for him to be seen in. He also had a purple dressing gown and was even wearing purple when he died.
Another wizard who encountered Harry also wore purple.
“A bald man in a very long purple coat had actually shaken his hand in the street the other day and then walked away without a word.”
The Knight Bus uniform is a shade of purple as well, and Ludo Bagman wears purple robes to the Yule Ball.
“Ludo Bagman, tonight in robes of bright purple with large yellow stars, was clapping as enthusiastically as any of the students; and Madame Maxime, who had changed her usual uniform of black satin for a flowing gown of lavender silk, was applauding them politely.” - Harry Potter and the Goblet of Fire
In fact, there's a Pottermore writing that specifically says wizards favor purple as a way of identifying themselves to each other.
Witches and wizards often reveal themselves to each other in public by wearing purple or green, often in combination.
Here is the passage from the book you are talking about.
[Mr Dursley] found it a lot harder to concentrate on drills that afternoon, and when he left the building at five o’clock, he was still so worried that he walked straight into someone just outside the door.
‘Sorry,’ he grunted, as the tiny old man stumbled and almost fell. It was a few seconds before Mr Dursley realised that the man was wearing a violet cloak. He didn’t seem at all upset at being almost knocked to the ground. On the contrary, his face split into a wide smile and he said in a squeaky voice that made passers-by stare: ‘Don’t be sorry, my dear sir, for nothing could upset me today! Rejoice, for You-Know-Who has gone at last! Even Muggles like yourself should be celebrating, this happy, happy day!’
And the old man hugged Mr Dursley around the middle and walked off.
Philosopher’s Stone - Chapter 1: The Boy Who Lived
The man has two identifying feature (three if you could the violet cloak). He is a tiny man, and he squeaks. Professor Flitwick is also short and squeaks, as seen in the following quotes.
Professor Flitwick, the Charms teacher, was a tiny little wizard who had to stand on a pile of books to see over his desk. At the start of their first lesson he took the register, and when he reached Harry’s name he gave an excited squeak and toppled out of sight.
Philosopher’s Stone Chapter 8: The Potions Master
Before Ron could answer, Professor Flitwick appeared at Malfoy’s elbow. ‘Not arguing, I hope, boys?’ he squeaked.
Philosopher’s Stone - Chapter 10: Hallowe’en
‘Now, don’t forget that nice wrist movement we’ve been practising!’ squeaked Professor Flitwick, perched on top of his pile of books as usual.
Philosopher’s Stone - Chapter 10: Hallowe’en
Therefore, I think it likely that Mr Dursley ran into Professor Flitwick.
Fun fact: The only other time Flitwick speaks in the book, he does so "softly" instead of squeakily.