I had a lot of issues with this and here's where I finally landed....
Mens electric beard trimmer for my underarms. (If you have fine hair you might get away with a ladies electric razor, but those are like cheap toys for my thick monstrous hair )
Ladies disposable single blade manual razor for my legs, or nair. Nair is good stuff. (Extra blades or pivoting blades always cut me, I dont like them)
Pubes: mens electric beard trinmer followed by Nair.
(In my experience Nair works better on stubble than long hairs, so it helps to either use it frequently or use the electric trimmer first)
I also have a small pair of cat grooming scissors for stray hairs that the razors or Nair misses. These are good because they are small, precise, and very sharp, but have blunted tips and a "tooth" so it cuts hairs effectively but not skin. (Pinching my skin isn't fun but I've never managed to break my skin with them).
I'm too chicken to try wax or epilators...
_________________
...what do the public, the great unobservant public, who could hardly tell a weaver by his tooth or a compositor by his left thumb, care about the finer shades of analysis and deduction!