There has to be an easiser way
 

When installing new styles for vBulletin. I import the style then I find myself copying all of my old modified templates to my computer as .txt's then reuploading them to the Admin CP for the new skin, and overwriting the old templates.

Is there an easier way or is this probably the best way to do it?

Have it as a child style of the one with the modifications?

Would that still allow users to select the style just fine?

Sure.