It is possible to castrate adult rams using bloodless castrators - you can do this yourself. The castrators are quite expensive, so probably best to find someone who has some and possibly they might even do it for you.
It works by cutting through the spermatic cord and blood vessels that supply the testicles., without breaking the skin. Because this is totally enclosed, there is very little risk of infection. You cut the chord in two different places on each side, just to make sure. The disruption to the blood supply causes the testicles to gradually shrivel up. You do have to keep an eye on them for swelling etc and check about 6 -8 weeks later to ensure that the testicles have shrivelled up and that the cords are still severed.

Its still not very nice, but not as unpleasant as open castration.