They make special hair removal products for sensitive parts of the body.
(Believe it or not, I know that because they just had them for sale cheap at Goodwill. No, I did not purchase any.)
If the bumps and blisters are an indication of ingrown hair, the same can occur with hair removal products.
And yeah, you can shave your balls. Just don’t get over-jealous. A nick will bleed forever – not enough to matter but hell on light colored shorts.
Next time you’re tempted, try trimming back the non-scrotal hair with scissors, then slowly gently shave your balls, and use the razor to ‘clean up’, er, “the rest”. Creamy Vaseline will keep the area (and the short-hairs) soft.