Is it possible to specifically select edge (only) loops?

Now you’re probably thinking, yeah there’s already an edge loop tool. Alt select, you fool!

But it’s got one problem that’s slowing me down with something I’m trying to model. It seems the loops it selects has more to do with having surrounding face geometry than the edges themselves. So if I have a smaller loop that is bridged only by edges (and possibly their connecting vertices) within a bigger opening that is surrounded by faces, alt-selecting fails to recognize it and selects only the bigger edge loop area surrounded by faces.

Right now I’m kind of manually selecting areas along shortest path, but it involves a few more steps to bring it to a full loop. So I’m wondering if there’s any way to select closed loops by shortest path and no need to respect having any surrounding faces? (So more like an edges-only version?) It’d greatly speed up the kind of thing I’m trying to model.

If this isn’t possible yet, note that this is not really a gripe about the current behavior. It’s just that having another option available would be nice.