What you're describing is a foul in Quidditch called a Snitchnip. It's defined as
Any player other than Seeker touching or catching the Golden Snitch
Quidditch Through the Ages
The implication is that interfering with the Snitch can cost you a personal penalty...
The referee may award penalties against a team. The Chaser taking the
penalty will fly from the central circle towards the scoring area. All
players other than the opposing Keeper must keep well back while the
penalty is taken.
Quidditch Through the Ages
...but not a sending off.
Down in the stands, Dean Thomas was yelling, ‘Send him off, ref! Red
card!’ ‘This isn’t football, Dean,’ Ron reminded him. ‘You can’t send
people off in Quidditch – and what’s a red card?’
...
‘All right, all right. Flint nearly kills the Gryffindor Seeker, which
could happen to anyone, I’m sure, so a penalty to Gryffindor, taken by
Spinnet, who puts it away, no trouble, and we continue play,
Gryffindor still in possession.’
Harry Potter and the Philosopher's Stone
And since the snitch (at least in competition play) has had its 'sense memory' interfered with, a new snitch will need to be brought into play.
‘Correct,’ said Scrimgeour. ‘A Snitch is not touched by bare skin
before it is released, not even by the maker, who wears gloves. It
carries an enchantment by which it can identify the first human to lay
hands upon it, in case of a disputed capture.
Harry Potter and the Deathly Hallows