Check these 3 things out ... found them after a lot of research for my chica so she could go off those little bikini razors
1) is any type of Panasonic electric shaver that's Wet/Dry and has the pivoting head. Usually these are $80 or more for the men's version but there's a girl's version (complete with being pink) that's more like $33 from the right source and although not advertised that way seems to be the exact same thing, including battery life. This one is on the same first charge from before Christmas two months ago with two people using it all the time. Reviewers who say they have to charge theirs every couple of days are either insane or shavingsheep dogs for a living. Panasonic ES2216PC. This could easily be all anyone would need. It is possible if going to fast to barely-nick your sack with this one. Even if you do manage that, from bad method, it's minor and still way better than tweezing. Pull your skin tight at the folds, or press a ball over to bulge the skin outwards, don't try to press the razor down hard enough to push the folds flat .. that's how you'll get nicked.
2) is the Cleancut trimmer PS335. This one is dry-only but super versatile. It's a T-shaped trimmer that pretty much can't nick you at all ... so the harder your press it into the skin, the closer and closer it cuts. Can do pubes, shaft, balls, brazil zone - ie taint/butthole, anything .. really fast and nick-free (even with not being careful about it). She can't stop telling friends about this one.
3) is same company (and Japanese, gotta love them for quality hygiene) the Cleancut ES412. Also dry-only. Can use with shave gels I think but not in the shower or underwater. This one is a circular spinning blade in a circular-shaped trimmer, and will get wax-smooth on you if you want to go that low. I would almost call this one overkill except, for me, some stubbly hair on the sides at my base (that are actually ok and only bother me) but to go skin-smooth on that particular area it takes the 412.
To kak03, the hair on the balls isn't very thick, comparatively, and the easiest way to address that stuff might be a depilatory gel like Nair or Veet etc. I haven't done that since my twenties, something about being a runner that made sense at the time, but the whole thing was a snap.