Switching from one mapping system to another will alter all of the mapped textures. There is no real way around that, - it is the nature of the differences of the mapping systems. Global mapping will stay put as the object moves causing the texture to slide across the object, whilst UV doesn’t, being fixed to the object. Likewise object mapping uses the co-ordinate system of a third object to define the texture space.
If you need to convert a global mapping to a UV mapping, then you need to bake the maps onto the object, using either your global co-ordinates, or the view point’s co-ordinates.
The UV unwrap feature allows you to unwrap from the current view, and then you can bake the textures to an image file from the current view, and when you re-apply them, you should get the same result on the UV image as you had on the global one. However, any parts of the object that are perpendicular to the viewpoint may end up with very stretched looking textures applied.
I won’t document how to do viewport unwrapping and viewport baking, as there are tutorials out there which will show you better than I could.