Why don't you want to use a razor?
You can only use the same methods anyone wanting to remove hair has the options of using.
Scissors, razor, electric shaver, waxing, epilator, hair removing cream, plucking or electrolysis.
From that list, a razor or shaver is the obvious easier answer.
The other solutions would just make life harder for you.

It doesn't have to be a full size electric shaver, one of these would do the trick: