No no no no no. Just no. Please let this not be a thing.
He looks quite decent on YouTube. He is quick, close ball control, can run with or without the ball and can assist. The rest would be up to Wenger to make sure he gets the best out of him. YouTube can be quite misleading but my initial reaction is go get him Wenger.
A little hint from Kokorin:
https://www.instagram.com/p/_tmNkLTLUi/?taken-by=kokorin9
Translation - "the last 5 days of vacation..."
All vacations in RPL will end only by January 8. It could mean anything but there are some insides in russian press about Kokorin to Arsenal.
The only reason I'd be optimistic about Kokorin would be Wenger's judgement. If he sees some material to work with there he could turn out decent. Giroud for all the hate he gets has improved a lot in his overall game and technical ability in 3 years or so.