This is going to sound a bit depressing so sorry in advance.
There are risks to surgery and these should be explained to you before you decide on this option. This include the risks of general anaesthetic as well as the shock from the surgery and trying to get them eating again afterwards. There is also a genuine risk of stones reforming in some pigs, but you don't know whether your little chap will be one of them... and tbh I'm not sure whether anything is known for sure about why the stones reform. They might be able to give you some indication of what their success rates are, and some idea of whether his relatively rare arthritis will affect his outcome.
Balanced against this is the pain and inflammation the stone will be causing him now, and the fact that things like bacterial urinary infection will be more likely and that with a large stone he might have pain when pooping (which seems to be pretty much a 24/7 activity). Your little guy has other issues, but he has youth on his side and in your shoes I'd be looking at finding a vet who feels more confident about the surgery option. If you go in with your eyes open and take a chance for him it could be relatively straightforward. It's possible the vet you spoke to earlier is working from their own experience - which may be limited to older piggies. The bare truth is that many people confronted with the prospect of paying hundreds for surgery, then committing to nursing their boy for a while, with a chance of ending up back at square one within a few weeks or months, or the alternative of paying 30 quid to put piggy to sleep here and now will choose the latter (again, especially if piggy is older) and that might be where this vet is thinking things will end up.
But nobody can predict the future and the best thing I can advise is that you put yourself in your own shoes a year from now and 'look back' on the choices and possible outcomes, and see how you feel. Hope for the best but prepare for the worst. Surgery is hard on them, but he'll have a chance: without it he won't improve and you're marking time till he declines. I'm really sorry for the position you find yourself in - he looks a lovely little fellow
And in case you're wondering yes, I chose surgery for my older boar to give him a chance, and I'd do it again with another although I hope not to be in that difficult position again. We'll be thinking about you x