I think maybe you're a little too young to take this task on by yourself, isn't your dad available to help with some of the heavy stuff? (joke!)
If the stator is roasted they most likely used too large of fuse and it's likely the diode bridge rectifier is suspect also. On the bright side, bridge rectifiers this size can be had for just about $3 in aftermarket.
Okay this is going back in time and so I must stop and say, what a nice time capsule! (and great (fun) ski).
I'm pretty sure this is a single phase stator (2 yellow wires), correct? If yes, the two yellow wires are for the AC input coming from stator to the full wave bridge rectifier then make sure the + output of the bridge rectifier has a reasonable size fuse maybe 10A maximum but more likely 5~7A is all that circuit can produce to charge the battery. the - terminal of the rectifier goes to ground.
The other two wires (of the four) would be for the ignition trigger, polarity might be important thus the wires should be color coded, aren't they?
At least that's the way I expect it's wired.