Yeah, I don't see hot wire as harmful. Barbed wire isn't appropriate. If you don't know it's there and take care to avoid it, it can really maim skin and ruin clothes. If you do know it's there, it's easy to avoid and not much of a deterrent. Plus it rusts, and that becomes a health hazard if it punctures skin.
But hot wire? I know TONS of people who use it on urban fences because their dogs climb fences, or cats come in the yard and either make messes or put themselves at risk of being killed by prey driven dogs, or to protect their urban hens from being killed by marauding raccoons. And yes, even to deter fence hopping neighbors. I don't see it as cruel to put one up, especially if kids get a heads up that it's there. If the kids decide to hop the fence anyway, well, they were warned.
I used to climb cattle fences all the time as a kid. They were combo barbed wire and hot wire. Barbed wire is totally easy to avoid. Hot wire nails you sometimes. It's annoying and stings, but doesn't even leave a welt. That's even if you do something stupid and land in the watering trough with your wet head touching the wire.
I would not approach them with ANY concern about the kids/dogs causing injury to each other. That's practically admitting that your dog has the potential to hurt a child. If something horrible DID happen, that can totally be used against you in court.
Personally I'd stick with things along the lines of, "The fence is old and not made to be climbed on. I'm afraid you kids might fall, or break a board and the dogs would get loose and run over by a car," etc.