Well, scor tape might work for you-- it is a double sided adhesive that can be torn or cut with scissors. Comes in multiple widths. If you have zero use of your other hand, you could probably hold the roll in between your knees and peel the tape back and tear it, or probably even work with it on its side on the desk, though it is occasionally a bit of a pain to pull off the backing. The downside is that the adhesive is very strong so you will only get one chance to put your item down.
I also like tombow mono liquid adhesive in the green and white bottle. I have a little time from putting it on to adhere my pieces. Also, it just dries to repositionable so even if it takes you a bit of time to flip it over, it should still stick.