B'ski,
May I suggest you look at outboard motors? Either on line or at a local marina. Most every electric start outboard in the last 20 years or more has an electric choke. Push a small button, the choke engages, turn the key and the motor starts. Release the button after a few seconds and a small spring not much bigger than a ballpoint pen spring returns the choke butterfly back the the open position.
Outboard motors usually run in the warmer months so you may have to hold the choke button in for a extra few seconds in the colder months. All it would take is 2 wires, probably 18 ga. or 16 ga. at most and a momentary contact switch next to wherever you put the starter switch.
Just splice into the 3 wires on the back of the key switch mounted on the generator and run them the 50 or 75 feet or whatever length you need thru your underground plastic pipe alongside the 2 wires for the choke. Connect an additional key switch and a choke button wherever you want your remote start location to be and you will be able to start the generator from either location.
If you have a marina nearby or know of someone with a junk electric start outboard you could probably get the choke selnoid pretty cheap and the necessary wire, key switch, choke button switch and needed connectors shouldn't cost all that much.
Simple, proven effective and cheap. Good luck.
