They really only need the bellybands for marking in the house. His "manhood" won't be affected by the neutering. It's his "jewels" that will be. Madison marked a lot in the house (outside, it doesn't matter really if they mark) before being neutered so I kept a bellyband on him while he was inside, took it off when he went outside (so he could pee without peeing on the band), and left it off at night or whenever he was just lying down next to me in the room.
Right after he was neutered, I tried not to keep it on him (and used a "onesies"....one of those one piece cotton baby outfits) b/c I was concerned that the back edge of the belly band might be rubbing on the little sac that's left (with nothing in it anymore) after his neuter and I didn't want it to get irritated or possibly infected. That little sac (unbeknownst to me previously) apparently sort of withers up, and it seems fairly thin, so I wanted to be careful.
If yours doesn't mark inside, I don't think you'd need a bellyband at all. Madison has almost completely stopped marking inside since his neuter BTW
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Is it normal for the vets there to give injections to decrease the hormones before neutering? I don't think they do that here....or at least, neither of mine got them. Interesting!
Oh...just for clarification: the onesies I put on him to prevent him from licking the surgical area and so he wouldn't have to wear a cone or "e-collar" for that purpose. I just unsnapped it and rolled it up when he needed to run outside to pee. Good luck!