Nut slot filing for a single string

Yes, you will likely need to file the slot. A standard round needle file should work for that job and will be far cheaper than a nut file, and can be found in most hardware stores, hobby shops, etc. An 1/8" chainsaw file would also work well.

 

Maybe. Why not find out first. Slide the string through the nut slot and see if there is any binding and check to see if the strings seats fully to the bottom of the slot. If in doubt about the latter, rub some pencil lead into the bottom of the string slot, slide the string back and forth in the slot and see if it removes any of the lead. If it does, the slot doesn't need widening.