JELQ with just one hand

The recommendation I saw here is to hold the JELQ with both hands, but I realized that using only the left hand I avoid hurting that large vein from the base of the penis

Can I use only one hand to perform the exercises?

That sounds like a Dry Jelq, more or less.
But if you mean to add a lot of pressure, then with just one hand, that’s actually what the traditional Uli #3 is.

Edit: Video links —
Dry Jelq Video
Uli #3 Video