I shoved my 130mm wheel into my rear dropouts that were around 124mm and didn't change anything else out other than the low and high limit screw settings for the derailleur since i went from a 6 speed freewheel to a 7 speed cassette. I didn't bother cold setting or anything. Works fine.

I think you are rather overthinking this. Just relax, shove your new wheel in place and possibly adjust the limit screws and go ride.