Offsetting only edges with valence 2

Hello together,

I got this mesh (only a part at the moment) and need to offset all edges with valence 2 on their coresponding faces.

I managed to do it with all edges but now im stuck getting rid of the edges with valence 1. I already tried to cull duplicates, but that also delets the needed segments with valence 2. I also tried to use Mesh Edges and oparate only on the edges with valence 2, but i didn't manage to get them offseted on their coresponding faces.

Any ideas?

Thanks all!

PS: after offesetting the points are used to generate nice stitchin patterns.