I don't think they intend for folks to replace the battery, but you certainly can. The unique issue is that they use a non-permanent adhesive on the Beacon nocks that I have (early versions) to help hold the battery in place. If you replace the battery you'll lose some of the adhesive. Sure, a drop of super glue is a permanent fix but then you'll never replace it again. Perhaps someone has a recommendation for replacement adhesive. Or maybe it will work fine for you with the residual adhesive left over from the initial battery.
Removal of the existing battery is quite easy. First, make note of how far the existing battery is inserted because you'll want to match it with the replacement. Using a pair of needle nose pliers, flip the nock over to the side opposite of the switch to the oval opening. Put one end of the pliers on the top of the battery and the other on the bottom of the nock. Press lightly and the battery will side down. You should be able to easily pull it the rest of the way out.
It uses the standard CR-425/BR-425/LM-425 battery. Hope this helps.