This sounds like an interesting project, but in the current form it's too broad for this board.
This could be a path to follow, if you run into problems, just ask here, but make sure that it's a closed question that deals with a single problem ("How can I simulate a button press on a remote with my ESP32- Arduino"):
I found this: discord-arduino-simplest which is a chatbot that runs on an arduino and turns an led on or off depending on messages in the discord-server.
send discord-message on wifi-arduino
Board wise: the Adafruit HUZZAH32 – ESP32 Feather Board is a good starting point. It has wifi and a battery-connector so you could add it with a small LiPo to the collar. Should be the size of a matchbox.
As you have experience with electronics, you should be able to analyse the receiver on the shock collar. I guess it only sends a signal to the shock-generator which you can also to with the arduino. If you do it right, the normal remote will still work.