Yes, there is a way. you can transfer uvs using transfer attribute. First, you will need to goto shapeOrig in attribute editor of skinned object and then uncheck intermediate object in object display. After that, you have to goto outliner and check shape. now you can see shapes and shape orig under transform of the mesh. Now select your mesh with new uv and shapeorig from outliner. choose the following option in transfer attribute,
now you should have similar uvs. To hide the shapeorig, you will have to check the intermediate object again.
Let me know if it works.