Welcome. Ricky Stators has quality quality replacement units, so does Yamaha. You can take your chances on a used unit on ebay if you don't like the price of those, but given the importance of the R/R, it's a good investment. There is a good chance that your R/R is still functional. Get the wire fixed
Regarding the wire...the spade connector can be removed and a new one placed on the wire and reinserted. If you are not comfortable doing that any bike shop can do it. If you do the repair you'll want to confirm that there is continuity in that wire after the repair. That red wire terminates in many places (it is the life-line of electrical power to all systems) but the easiest place to check continuity would be between that wire and one of the fuse (red wire) connectors. Remove a fuse and one of those sides is connected to that wire. If you have continuity then the system will be charging. Or you can just confirm that the system is charging...but I like to check my wiring before I ask any work of them.
Also, that wire is showing signs of corrosion (the green stuff) - that's why it burned up. My guess is that the connector side is showing a lot of corrosion. The corrosion causes poor contact, which causes resistance in the line, which causes heat...and there you are - burned wire. So clean that connector up with contact cleaner and use dielectric grease on the connector and the R/R.