When I play, the skins only show up for the person applying it. I would like for the skins to show up server-wide so people other than the person holding the skinned item sees them. Is there any way to do this?

It should be. Just wait or change load timeout. Check your F1 console (on client where you don't see the skin) and gimme the output

Nevermind the skins were just loading in fairly slowly. Sorry bout the inconvenience :)