I have never found narrow enough double sided THIN tape (plenty of double sided foam tapes, but these are too thick.) to do the repair. You could find wider stuff, let most of it hang over the glass and trim it off with a razor blade, but the stuff loves to stick to anything.
My favorite double sided tape is what they use to weatherize windows with the plastic heat shrinkable film, they sell long replacement rolls of it in home improvement stores and the glue will release if needed.
BUT in your situation, I use a contact cement that is manually applied, and I do not wait for it to become tacky - I reassemble right away. I have not tried to disassemble a finished one, nor have I had reports of any of them coming loose on the units I do not possess. I would not trust any double sided tape I have been able to find to do that.