I'm not really sure. The more official sources seem to have in mind a full use of a patch, which I'd guess involves removing the full backing; people on Longecity discussing cutting up patches seem to think that you can cut up some brands of patches without too much of a problem and there will only be evaporation from the cut edge (but this is still fast enough that you might want to seal the edge somehow or use the cut patches within the week).

You could try removing the backing from some and then, 'several days' later, seeing if they feel the same as the usual ones.