Hi Alexander,
There is nothing that can be done to solve this. It is a security feature of ASP.NET that the control tree on postback must be the same as on the initial request. This prevents malicious form tampering. When the skin is changed the control tree is changed and one must refresh the page again before making a postback.
Changing of skins "should" be a relatively infrequent activity so it should not be a big problem. It can be wise to change skins at a low traffic time of day or notifying users ahead of time to save their work and make no changes until after the skin change is complete.
Best,
Joe