Have 2 current doorbells (front and back doors). Want to install one Ring Doorbell on front door. Will the back doorbell also be disabled?

I have two existing doorbells (front door + back door) and since each rings the same chime, twice for front door and once for back door, I believe there are two sets of wires connected to the chime (need to verify). If I install a Ring Doorbell on the front door and use the Ring jumper wire on my chime, I believe both existing doorbells will be disabled. I'm thinking I can disconnect the front door input wires to the chime, bypass the chime and hardwire directly to the transformer, thus getting necessary power to the new Ring Doorbell. I'll leave the back doorbell inputs in place, which will allow me to still use the old chime for the back doorbell. Will it work? Feedback?