Based on the amazing work sidoh10 created: https://www.thingiverse.com/thing:3079607

As suggested by sidoh10 tutorial, is possible to open amazon dash buttons to replace the battery. This operation is unfortunately irreversible so a case must be created to replace the original one. I feel like the amazon dash button works better if the original plastic top cover is left (the button movement is smoother), so I created a slightly modified version of the bottom case which snaps over the amazon dash and doesn't require a top cover.