So you are thinking of mechanically moving the manual switch with a remote control servo, right?
Just one quick thought, ever think of making your trap autonomous?
Meaning, you have a sensor that detects the bird or whatever and just springs it by itself, while your busy eating pizza and filming squirrels or whatever . . .
This article should help you go remote control:http://www.societyofrobots.com/remote_control_robot.shtml
You just hook up a servo to a reciever. The reciever hooks up to a battery. And a remote sends commands to the reciever. The HS-311 servo is the cheapest in the market.
In terms of simplicity you may just want to consider getting 200yds of wiring. When they blow up buildings everything involves very long wires connected to a switch . . .