My first advice is to never, ever leave your baby unattended with any bone or chews, ever. They are ALWAYS a choking hazzard. My boys get their chews only when supervised. Yorkies have died from choking - so I just really want to point that out for you, I'd hate to have you learn the most awful way.
It's hard to say what's going on here - did he have teeth pulled during the surgery too? It sounds as if he is swallowing these chews when they are too big - and it may be bc his mouth is still sore - and he's not chewing them as he should be, then he vomits.
My Marcel vomited for many days after surgery, but he felt just great (100% appetite, 100% energy)! I finally figured out that bc he is a "tiny" and his throat is so small, I think his gag reflex nerve bundle actually became irritated from intubation - and it was senstive/irritated for about a week+ following the surgery. I don't know if that's possible for your guy or not.
Hope he feels better soon!