Hoof nippers for the ergots. Clip, clip and you’re done. A cheap pair of nippers is nice to have around anyway. I haven’t had a horse object to trimming them back, but I don’t go super short. Whatever they’re doing (if anything), they don’t seem to be any more functional by being longer.
For flakey chestnuts I run the curry comb over them every time I groom and that keeps them in check. I’ve seen horses with more solid, rock-like chestnuts but haven’t had to deal with that personally.