Try below code to set page skin
                  Dim objTab As DotNetNuke.Entities.Tabs.TabInfo = New DotNetNuke.Entities.Tabs.TabInfo()
                    Dim ctlTab As DotNetNuke.Entities.Tabs.TabController = New DotNetNuke.Entities.Tabs.TabController()
                    objTab = ctlTab.GetTab(tabId, portalId, False)
                           'for skin set ,you can use this       
                         objTab.SkinSrc =" your skin value"
                         'for container set ,you can use this
                         objTab.ContainerSrc = =" your skin value"
                       'save settings
                        ctlTab.UpdateTab(objTab)

                            

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Ok.For full solution, I think you need do these works.

1:Create a table to store data

2.Create a module to let user select their favorite skin.I suggest this function open for both register user and anonymous users.

3.Save user selection, for register user,save it with database, for anonymous users,save it to cookie.

4.Create a module to apply skin selection. much like this.

           If (GetUserSkin(UserId)!=null&&Request.Params["SkinSrc"]!=null)
          { 
                Response.Redirect(Globals.NavigateURL(TabId, "", "SkinSrc=" + GetUserSkin(UserId));
          }

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Over 20 + professional dnn modules for News Article, Store, Video Gallery, Photo Gallery, Ultra Flash Player,YouTube Video, Image Slide show, Skin Chameleon and much more from DnnModule.com