I think this is unanswerable.
I don’t think wandlore in the HP universe is sufficiently well-understood to cover this scenario, which was fairly unique. I’m also unaware of J.K. Rowling commenting on this.
You’re correct about the twin cores. In fact, Ollivander remarks upon this fact when Harry is buying the wand:
“I remember every wand I’ve ever sold, Mr Potter. Every single
wand. It so happens that the phoenix whose tail feather is in your wand, gave another feather – just one other. It is very curious indeed that you should be destined for this wand when its brother – why, its brother gave you that scar.”
— Philosopher’s Stone, chapter 5 (Diagon Alley)
Later, we learn that Ollivander tells Dumbledore about the twin cores, possibly because they both came from Fawkes, or perhaps because Dumbledore is the only match for Voldemort, and this may be useful information to him.
When Harry meets Ollivander again in Deathly Hallows, it’s emphasised just how little is really understood of wandlore:
“The wand chooses the wizard,” said Ollivander. “That much has always been clear to those of us who have studied wandlore.”
“A person can still use a wand that hasn’t chosen them, though?” asked Harry.
“Oh yes, if you are any wizard at all you will be able to channel your magic through almost any instrument. The best results, however, must always come where there is the strongest affinity between wizard and wand. These connections are complex.”
— Deathly Hallows, chapter 24 (The Wandmaker)
In the same chapter, we have lines like, “subtle laws govern wand ownership” and “wandlore is a complex and mysterious branch of magic”. Perhaps most telling is this passage, when discussing Voldemort using Lucius’s wand:
“I had… never heard of such a thing. Your wand performed something unique that night. The connection of the twin cores is incredibly rare, yet why your wand should have snapped the borrowed wand, I do not know….”
— Deathly Hallows, chapter 24 (The Wandmaker)
As Ollivander says, I think this is a unique situation that isn’t understood by wandmakers. We know that part of Voldemort’s soul is embedded in Harry, in a horcrux-like fashion. Nobody else is ever known to have created more than one horcrux, which means it’s unlikely that anybody else has embedded part of their soul in somebody else. (Possession aside, which seems quite different.)
Wandlore is complicated enough with a single soul; almost certainly the case of a soul-and-a-half jammed into the same person would never have been studied or understood. In fact, it’s quite possible that the effect of non-living horcruxes on wandlore has never been studied, either.
As @Simon points out in the comments (and I forgot to mention in my first draft), we also have the rarity of twin cores. That alone is pretty unusual, so who knows what happens when you throw poorly-understood horcrux magic into the mix?
So you might be right: the wand which chose Harry may have been influenced by the fragment of Voldemort’s soul inside him. But I don’t think wandlore in-universe is sufficiently well-understood to prove or refute that statement.
