Would you expand on your post, so someone knowledgeable may be able to help? I don't understand, are they at the vets and he isn't releasing the cats for pick up? In which case, definitely leave them there until it is safe to bring them home.
Or were you told once you got them home, you personally can't pick them up for cuddles ect? If so why were you told that & for how long?
If one is a boy you don't have to be careful about picking him up. No internal surgery there---just snip snip!
For girls you do have to careful of their midsections for awhile. Don't pick them up around the abdomen for at least a month. But there are other ways to pick up a kitty---by the chest and back legs, for example, or sideways, the way someone might hold a lamb or large dog.
Yeah, I always pick the up like under their back legs and bum, just as long as you don't get them under the belly you should be fine. The boys should be okay, although I was overly careful with Shortstack after he was neutered because he was older and had a bit more going on back there with his tomcat bits (which by the way, never really shrank--you can tell they are missing something, but he still has an empty furry coin purse back there!!!!!)