Re-powering a mower is by far and away a better alternative (less cost) than buying, presuming the TC mower you got is in decent shape.
It's not rocket science, but it does depend upon how much you want the safety controls to be interactive. You are correct in that the dealer wants to sell you a new unit rather than save you money.
Small engines need very little in terms of running; 12v power to starter and ignition with circuit interruption to eliminate battery drain at shutdown. A charging loop for the battery. A separate circuit for the electric PTO. That's about it.
It's all the interactive permission loops (seat safety, movement control safeties, blade engagement safety, etc) that complicate the issue. If you don't fear the operation of the unit and trust yourself, then many of those safeties can be removed. I am not advocating you do this in any manner unless you have full, complete, adult understanding of the risks associated with such endeavors and can accept the potential consequences, legal and otherwise..
I once re-powered an older lawn rider with a different engine I got from SEW. All I did was put in some simple switches:
- one toggle switch to ground the ignition (to stop engine from running). This is "open" for the engine to run and then closed to ground the ignition to shut it off.
- one toggle switch to engage battery circuit (to charge while running and not drain battery upon shut down). You close the circuit to charge batter and open circuit to prevent parasitic drain when off.
- one momentary switch to the starter circuit. Close the circuit to engage starter/solenoid
It is literally that simple. (I mounted the two toggle switches with their orientation opposite when side-by-side. In effect, the "up" position was open for one and closed for the other, so that when I wanted it to "run" of "off" I just had to flip both switches the same direction at the same time. The starter button was mounted nearby. This old mower arrangement still works to this day.
Now, if you get a replacement engine, it will certainly work as long as the clutch works on the shaft size (although there is no reason you could not get a different clutch ...) However, the wire harness is likely to have some different configurations. It's not that the wires needed will be different, but they may be in different positions in the harnesses and/or the harnesses may have different shapes. That's is what complicates things for some folks.
Not to be harsh, but it sounds like you're not up to the task; if you were you would not be asking. If you can read a schematic, then get the manual for the Scag you have for the chassis wiring, and then look over the engine power manual from the engine you choose. It should be no problem to trace out wires by function and splice them into the vehicle harness. If you cannot do this, find a local shop that can. If not, then you're stuck with getting another mower.
As far as selecting an engine, most of those warehouse places can offer advice in terms of "equal/alternate" motors to choose from. Get a few more ponies if you want. Or don't. When you re-power, the world is your oyster.
An important thing to not neglect is making sure that the new engine either has a muffler, or your old one will fit, and will that muffler fit properly on the chassis of the mower?