Can non-members in Runescape wear a skillcape of any non-member skill?

No a non-member cannot wear a ring of stone or any other member item, when you take a member item from a Member server to a Free To Play server, the name of the item changes to "Member's Item" (regardless of which item it is) and it cannot be used. If you have Member's Items equipped when you transfer to a Free To Play World these items will show, but they will provide no combat stats.

The only way to use something that resembles member's items is to get Corrupt Dragon items. They are identical to dragon equipment only members can use, with the exception of not being able to perform special attacks. Unfortunately, most of them cost a few million and it disappears in thirty minutes.