Sometimes, we have to travel outside of our areas to find a good rabbit savvy vet. So you should start researching and hopefully you can find another vet that isn’t too far away to do the neuter surgery. Even after neutering, your rabbit may not want to be held. Almost no rabbits do like it, since they are prey animals and it scares them. I never have picked up any of my bunnies unless it is really necessary. I let them come to me and sit beside me when they want to, but I never try to cuddle with them. A rabbit can severely injure himself, even break his back, when struggling and thrashing around, trying to get out of someone’s grip. And of course, they can inflict scratches on anyone trying to hold them. That can also cause them to be injured, if the person holding them drops them due to being scratched. So try to limit picking up or holding your rabbit. It’s safer for everyone.