Have mechanical butler's bell, would like to ring it with push button
I would avoid the wiring and go for the wireless switch and solenoid puller from a bell transformer. various solenoids are noisy or linear motors with soft end stop snubbers are quieter like in HDD VCM voice coils. off 12V supply.

https://www.youtube.com/watch?v=3ZUh2mp2Hc8

Or use a linear wireless servo controller that can reach with a front door lever connected to a pot with a spring.  The pot would have to enable a battery operated switch to transmit the servo position to conserve battery power.

"May I have some Tea daneee."

"yes my lord"