There are many concerns about wild rabbits at pets, Take a look at my answer at
Can I make a baby wild rabbit a pet? Given your description, of the behavior it very possible that you have domestic rabbit who is brown with a white tail and was in the wild when found.
Putting aside all of the issues of cotton tail as a pet, and just discussing the having a pet male rabbit neutered.
Realistically if the rabbit is always going to be in captivity and never exposed to other rabbits. the biggest reason to neuter is to modify behavior RE: How do I discourage rabbits from spraying?
The most common reason to neuter is related to rabbits making babies RE: How fast do rabbits really breed?
Female rabbits are definitely more at risk for cancers if they have not been spayed. I have not heard of an increased cancer risk for males. I defer addressing that at this point.
The third most common reason for neutering is housing rabbits in the same structure. Rabbits are very territorial and have high sex drives. An unaltered rabbit in the same building will cause negative behavior changes in the other rabbits in the home. This is the focus of my answer.
It is not the neutering that is risky it is the anesthesia. The risk is definitely higher with rabbits than other animals. So considering this is an important part of the decision. I don't know what the real risk is, but I would guess it is between 1 in 100 to 1 in 1000.
Age at exposure to anesthesia can make a difference, all things being equal younger (but mature) is less risky then older.
You should consider neutering for these reasons.
Boarding, if you go on vacation, to the hospital, or anyplace where you can't take your rabbit. If you can't get someone to come to your house, you will be looking to find a place to board him. In my area this usually occurs through the local group Rabbit Wranglers your rabbit goes to someones home who has rabbits and they watch him while you are gone. For all the reasons above it is more difficult to place a rabbit who has not been altered for boarding.
Bonding, if you decide to get a second rabbit as friend, it is strongly recommended that both have been altered for at 30 days before introducing them.
Behavior, Neutering modifies behavior. This behavior tends to develop as the rabbit ages. A neutered rabbit is much less likely to develop poor behavior as it ages. Neutering and altering behavior on an older rabbit brings more challenges.
Rescue, if you die or otherwise become unable to care for your rabbit, he will go to a rescue. At which point he will be neutered, during this very difficult time this is one less stress he could do without.
In summary; Yes there are risks, they are real, you are right to be concerned. While you don't NEED to get him neutered today, anymore then you needed to get him neutered yesterday. It is all the tomorrows, of which the are probably 8 to 12 or even as many 16 years more ahead for you both. You need to neuter him for unknowns of all of those tomorrows. The best age is 4 to 8 months, optimally at least a month before any of the 4 events above. Your are intelligent enough to recognize the risks of anesthesia, so I know you are intelligent enough to recognize the risk of one of those other 4 things occurring with less than a month warning. Sooner is better, I think you should make an appointment for the neutering as soon as you see he is male.
- Most Common in this answer is based on my personal experience.
