Rattler venom can damage nerves.
Grandpa was bitten on his hand almost 100 years ago, no antivenin then.
He reached absentminded for a burlap sack someone tossed by the chicken house door and there was a rattler under there.
He always said he knew better, should have moved it with a stick first.
He made it to town, where someone drove him to the hospital.
They treated him best they could those days.
He lost the use of that arm for two years, until most nerves regenerated enough to give him back some use of it.
I wonder if that is part of why your cat is wobbly, the nerve damage in some places from the venom itself and if so, it will take time, but he should regain good function.
The news reported this week that a two year old girl was bitten in her yard in town, was flown to the regional hospital, where they gave her 10 vials of antivenin and she is coming around well now.
Snakes are very thick and active this year, everyone is complaining about it and warning to be careful.
Sounds like your cat is doing ok now, that is great news.