Removing the 1970's era Western Electric model 1750 panel telephone from the kitchen wall
I plugged the hole with a custom shaped block of wallboard and some spackling. I left the button that used to unlock the front door for visitors.
Spackling was too thick to smooth out, but joint compound was like pudding and made smoothing much easier.
I tried painting just the patch, but as good as paint matching technology is, it just doesn't match exactly. So the next day, I taped everything off so I could paint the whole wall.
Jim, here is a circuit diagram for the 1750 telephone I got from PDF file 502-706. It may help with the next steps.
I found some instructions online for converting an old phone into a wireless by taking apart a wireless handset and tying it into the mechanical parts of the vintage phone.