Should I neuter my cat after just moving or wait?

My boy needs to get neutered, and I have his surgery scheduled for next Friday Feb 27th, but we just moved into a new place a week ago and my roommate moves in next weekend on the 1st.

He was originally going to move in sooner, but has pushed his plans back twice and decided the same time my boy would be getting neutered is the best plan, but is now telling me I should cancel and reschedule the appointment because his moving will probably stress out my boy and make his recovery harder and worse.

I would consult his vet about it but they have made it clear before their concern is nothing regarding his stress and mental health, purely physical health and my roommate said my vet will likely insist keeping it the same just so they can perform the surgery and everything else won’t be cared about.

What should I do? Any vets on here who can advise whether I should hold off for another month or just get it done? My room isn’t exactly laid out like a safe space for him yet…

For his health and details of my cat for better understanding, he is 3 years old on Feb 27th (happy birthday bud) 10-15lb, and he does inappropriate pee but doesn’t spray. He has pretty moderate separation anxiety as well so I medicate him for that, but sometimes it doesn’t work enough especially during stressful periods like this.