coyote call with 2 way? project questions.

Thanks for taking the time to check this thread out.
I’d like to make a wireless coyote call. I was thinking I could use 2 way radios.

One radio would be hooked up (receiver) to my battery powered amp and speaker. this end would be hidden in the field.

The other radio would have my MP3 player plugged into it. That way when I hit the “talk button” it would send the rabbit in distress call to the receiver.

Sounds good in my head :).
My only questions are: Will the sound quality be good? How long will the batteries last? Can I find an affordable 2 way that doesn’t BEEP when the talk button is let go.