Entropy,
You don't have any duct tape?
Take a close look at the switch. There are three contact points you need to find. When the switch is turned to the left it connects to the left contact, call this "A". When you turn it to the right it connects the right contact, call it "B". The center contact that moves up and down with the switch probably connects to the flasher, call it "C". Each of these three contacts has a wire that leads to the 4-way flasher switch. The flasher switch simply connects them all together at once.
Now, to replace that with a remote flasher switch, you can extend the existing wires, or intercept them at a point closer to the new switch location. The problem is that most switches are single throw, single pole and only connect two contacts together at once. You need to buy a single throw, double pole switch. Wire "A" to a "NO" (normally open) contact on one side of the switch, "B" to another "NO" (normally open) contact (next to "A") and "C" to both (common) contacts on the other side. When you flip the switch, all three should connect togther and provide flasher power to both sides of the car at once. When the switch is off, the turn signals should work normally.
The switch has to handle about 6 watts for each bulb so it needs to be able handle about 2 amps. You can buy a NKK S21F toggle switch from
http://www.DigiKey.com under their part number 360-1209-ND for $7.02. This switch has standard spade terminals and a 1" toggle. If you browse the DigiKey catalog you can pick from hundreds of switches, including lighted ones, rockers, push buttons, and solder terminals.
Paul