This is my opinion: I think you should bring him home with you now. He’s going to be stressed out regardless, I assume neuters are not much fun for a bunny… at least this way, when he gets picked up from the surgery, he will be going to a place that already smells like him, a place that he has had a couple weeks to familiarize himself with, and to people who are not total strangers to him. You don’t want his first real experiences with you ones of you having to check his sutures and give him meds when he’s not feeling well. He’s going to be ticked off about the neuter anyways, no matter whether he goes home now or later.

If you had an existing bunny that he was being adopted for as a mate, my advice would probably be the exact opposite. But in this case, I think it’s a good idea. Be aware, his litter habits might not be perfect as he’s in a new place and still unneutered, but this is only short-term.

Edited: I don’t remember, aren’t you the one with the partner who may be allergic to bunnies?  In that case, I think it’s a good idea to do a trial run anyways, with the bun in the house to see how she reacts.

Well, a shelter environment is always more stressful.

I agree. Bring him home now. He can get used to his new home then feel more comfortable during his recovery post surgery. Plus, you free up a shelter space for another bunny. Are you still getting the female also?

I double triple ditto ditto! Bring him home now so he can get comfortable and familiar with you and your partner and your place. That actually may make his recovery less stressful because he would at least have some time with you beforehand and then come back home with you and your partner for a loving safe place to heal.