Fuzz in jag?

Thinking about building a fuzz face into the rhythm circuit of my Jaguar- anyone do this or something similar? It’s a fairly compact circuit so I think I should be able to get away with it, but I’m interested to hear any insight from people who’ve tried doing something like this on any tips to make it work! The idea would be the switch would turn it on and the volume and tone would serve the volume and fuzz functions. My only worry is that the battery would be constantly draining when the guitar is not in use, any way around that? Cheers buds!