By creating an UV map for the basemesh that is compatible with the old textures.
Then you can use Blender to bake between the two UV maps and bake new textures that are compatible with the new mesh by default.
The nightlies of MH (perhaps 1.0.2 as well, I have not checked) already come with such an A7 UV map for the basemesh. It's in the file data/uvs/a7.mhuv and it's basically an OBJ file with the vertex data stripped out.
You can load it on your mesh using the material editor, and loading the file as UV map on the skin.
Export the model with this UV map, and then with the original UV map to blender and you can bake between the two.
Note that the mapping is not perfect, and you will need to do some corrections in a photo editor.
Also see:
viewtopic.php?f=6&t=9869&p=21325&hilit=uv+map+material+editor#p21325viewtopic.php?f=13&t=10789&p=24495&hilit=uv+map#p24495