If you really cannot damage the patch in any way by sewing or gluing it, the only choice I can think of is glass encapsulation.
Have them professionally framed in a vacuum-sealed glass "sandwich" of two sheets held together by a frame.
However, if the patches are vinyl-backed (most are) then glue dots from a craft store should work without leaving any damage. They are a flexible solid, and you can just rub it off in a blob with your finger. (Same stuff that holds new credit cards in place when they mail them to you.)