I know of some veterinary clinics that have closed in the past year there.
Two of them are the Menetar and the Greyhouse -clinics.
Greetings The Freak
The neuter will be nothing. The move will be the big deal because cats just hate change and it upsets them. Crate him up, put a towel over the crate to keep it dark and cozy. Dark helps keep the stress level down. If you want to help even more, go to the pet supply and get a spray can of Feliway. It is a pheromone that the cat can smell but you can't. It's a calmative and you give 2 or 3 spritz into the carrier and cover with the towel. That should settle him down very nicely. It lasts about 2 hours so if it's going to be a long day, you may have to spritz a few more times. I got this product from my vet so it's well known and dr. recommended. I use on my cats for transport to the vet and the vet has used it on one of my cats during an exam when she was scared silly.
Put the cat carrier in the bathroom and shut the door and keep the cat out of the traffic area when boxes and furniture are being moved into the apt. When everyone is gone then take the cat into the bedroom and shut the door. I would not let him roam the apt because it will be spooky for him so just let him settle in for 2 or 3 days in the bedroom with litter box, toys, food and water then when you let him out be with him.
When he comes home from the vet after neuter, he may still be under the effects of the anesthesia and antsy. Don't let him out to wander as he can walk right into a wall like a little drunken sailor. Just keep him in the crate with the towel and check on him periodically but let him sleep it off.
A shelf attached to the window sill is a great place for a cat to enjoy the new views! Have a great move and hope everything goes well.