Is it imperative that the accession numbers be applied directly to the badges? My first choice would be to store each badge in an individual envelope or folder marked with its accession number. This could also prevent the badges from sticking to each other in the event that the adhesive is unintentionally re-activated (you might also want to add a release layer such as polyester film to prevent the adhesive from sticking to the envelope). This approach would work best if the collection is well cataloged, with images and/or unique descriptors of each badge linked to its accession number.
If the numbers must be directly applied, I wonder if you could iron twill tape labels onto the heat-activated adhesive on the backs of the badges (using a small heated spatula or tacking iron so that you are exposing the adhesive to heat only where necessary). This doesn’t seem ideal as it’s not reversible, but depending on the size of your heated tool you could experiment with using only small “dots” of heat to tack the labels to the badges.
Would either of these options work for your collection?