If you remove the USER object from your skin the users won't be able to access their account information completely. Look for <dnn:User runat="server" id="dnnUser"> in your skin ascx file.

This is probably more than you'd like, but there isn't a setting that allows you to turn off just the Profile Management. If you want to remove specific fields in profile management look to change the field from being "visible."

unfortunately, it is not as easy as described, even if removing the link from the page, a knowledgable user is able to append ?ctl=register to enter his user account. AFAIK the only solution is  using a costum or 3rd party user account module with advanced permissions. sorry.