Thats pretty old. It will be a painful and long ordeal if you decide to band them. I would recommend a different method at this point. Talk with your vet about options.
It depends on how big the testicles are. If they are mini goats it may be doable. If they are standard size goats probably not. I have banded some fairly well developed bucklings though. Pull the scrotum through the band first and then work the testicles through one at a time. Be sure to give a tetanus shot. It is very important that you get BOTH testicles.
Thank you for the replies. Based on the feedback, I will not band them. They are minis, but one of them has a pretty big set on him. It just seems too......uncomfortable to go the banding route.
Just a comment. You know how well developed your bucklings are and I don't. However, if they can be banded the discomfort only lasts a couple hours or so, if that, At least that has been my experience.
I've had a vet castrate a few by sedation and cutting. It wasn't any less painful for the goats. So no matter how it's done they are gonna be sore for a while and you will need to watch for infections.
You could get the vet to give them pain meds before banding. That way by the time the meds wear off, the circulation is cut off and they are pretty numb.
Banding in my experience is the best way to go. My little Buck was 6 months old and I had the vet do the procedure. Levi didn't act like anything even happened. Pain meds and local freezing were given. They fell off in 7 weeks with a nice smooth clean underside.