Chad: The issue with the KT17 to Magnum engine swap is converting the wiring harness to work with an ignition fired by a magneto instead of a coil. A coil, as found on the KT17 motor, requires positive battery voltage (from the ignition terminal on the ignition key switch) to operate; a magneto, as found on the Magnum motor needs only the motor to be turning over to operate, but it requires a connection to ground (preferably activated in some fashion by the ignition key switch) in order to "kill" the motor. (Whatever you do, be sure to have a way of grounding out the magneto while you figure out how to wire Magnum, or not being able to stop it will drive you crazy.)
So, there are basically three options for installed a Magnum motor in your 682:
1. Wire up a separate, manual, "kill" switch to the magneto so you can turn the motor off.
Note: With this option you can leave all the interlocks (seat and PTO switches) in place, but they will not function, because the connection to the ignition is lost (the connector at the coil just hangs there in space); the hour meter will work, though.
2. Wire a relay in series with the magneto. Use a relay that has a Normally Closed terminal (not all 12 volt DC relays have this terminal), connect the magneto "kill" contact to the Normally Closed contact, and wire the Common terminal to ground.
One advantage to this arrangement is that the function of the interlocks is retained, the motor will drop out if the PTO is switched on and the operator attempts to get off the tractor (that is, get out of the seat). The down side is finding somewhere to mount the relay and it requires some above-average knowledge of electrical wiring to get the relay operating correctly. Like I said above, be sure you have a way to kill the magneto until you're sure you have everything the way you want it. Another upside to this option is that you don't have to buy another ignition switch or in any other way modify the existing wiring on your tractor (other than the relay). It is the option I chose when I dropped the M18 in my 782, which I'm told is the same as your 682, except that it has hydraulic lift.
3. The third option is the one which Matt Gonitizke chose below, wire in a new ignition key switch designed for an engine with a magneto-fired ignition. The key for a magneto-fired engine does not have an "ignition" contact at the key, it has a ground contact instead, because, again, the control required for a magneto-fired engine is that one must be able to turn it OFF-it runs by itself, drawing energy for its coil by interacting with field of the magnet rotating on the flywheel of the engine.
It is easy enough to wire the magneto-style key into the circuit: just run a new wire (my preference) from the key's "M" terminal to the magneto and make sure your hour meter and oil light (if you have one) are wired to the Alternator's "R"ectifier terminal at the key switch.
The upside of this arrangement is that there is no relay to mount, or relay-related issues to trouble-shoot (like sticking contacts, burned out coils, mis-wired contacts upon re-assembly, etc., etc.)
The downside, for me, is that I'm not sure how the interlocks for the PTO and seat switches would be retained. I'm sure they can be, because I once owned an off-topic tractor that had both a Magnum motor and an operating seat switch, and I know that Cub Cadets were built with M18 motors and their seat switches worked too. My off-topic tractor used a relay, and I suspect that one would have to be used in the circuit in order to retain the function of the interlocks. (I like the way the later 1811 tractors were wired, they didn't drop out the motor, just the PTO.)
But if you don't care about stopping the driven equipment when you get off the seat, and you don't want to mess with a relay, and you don't mind dropping $40.00 on a new key switch (or you have one lying around), this can be a good option for you.
I hope I've helped. Given the description of your options above, if you tell me which one appeals to you, I'll try to give you specific instructions.
Also, as Roland Bedell would point out, if there were two versions of the 782 wiring, there are likely two versions of the 682 wiring, so we need to know if the serial number is below 720,000; or 720,000 and above.