Hi, the one to give you the best answer is the vet who is doing the procedure. Mine is just a guess. But here goes: I would say yes, with the vet’s confirmation of this needed. A neuter of a male is not as difficult as a spay of a female, and usually goes well and heals a bit faster. Your average neuter requires the first few days of close attention (watching for redness, swelling, or other signs of infection or illness). You need to keep your bunny from jumping up, so keep him on one level to assure healing without complications. He won’t lose his hormones internally for about a month, so he cannot be near an un-spayed doe during that time. However, other than getting a little aggressive during that month, he should be completely healed if all goes well within a week. Depends also on what kind of stitches are used, dissolving or those that need removing. Again, that’s a follow up with your vet. If he does get infected or something goes wrong, then you’re dealing with an unhealthy bunny and that might make it a high risk.
As far as being in an airplane, I don’t know if it effects his health that soon after a favorable neuter or not. Again, call the vet asap to ask.