How can I create a new skin for Tabbar?

Is there any documentation for styling the Tabbar skins? I would like to create a new skin which modifies dhx_skyblue to get rid of the background tabbar to the left and right of the actual tabs (like in default and modern).

No, there is not such a documentation. You may modify the following css:

.dhx_tabbar_zone_dhx_skyblue .dhx_tabbar_row {
border-left:1px solid #B6CBDD;
border-right:1px solid #B6CBDD;