Tricky one, I would also err on the side of 'no' - an unneutered male is likely to really harass a spayed female and that could easily result in a very stressed female and a big fight. They often get on the wrong end and hump heads too when they get excited and a female could easily bite his 'bits'.
Both of these options could result in the need to put the male under a GA anyway if he sustains injuries as a result, so if there is a valid reason why he absolutely can't have a GA, I wouldn't risk it as the end result of trying to do this bond is highly likely to result in the need for a GA at some point in the future.
Is the little chap in question likely to always be too poorly for a GA? Is there a possibility that he could be done by an exotics specialist who uses sevofluorane instead of isofluorane for a GA? When we're talking about a health risk, are we talking a huge risk or a small one?