Honeywell battery chime with wired Ring doorbell 3

I have a mechanical door bell which sounds like bizzz or buzzz. The sound is annoying and I’m thinking to replace it with a Honeywell DW313s. Wiring is difficult for me, there is two cables going to the mechanical chime. I’m thinking to use this doorbell in battery mode and connect those cables to A1 and A2 Do you think it will work? This is the model: https://livewell.honeywellhome.com/en/doorbells/dw313s/ This is the the wiring guide, page 2 is the battery: https://livewell.honeywellhome.com/honeywell_wp/wp-content/uploads/32310682-001_Rev_D_WEB.pdf This is a photo of my current chime: