unfold

[micheus]

Ok. I was thinking you were still looking for some automation.

In this case, what you need is already available.
If you proceed this way - selecting only the edges to keep and cutting everything else, you just need to use Selection-Invert:
a) in Geometry window, context menu set the invert the selection, set the edges to Hard Edges and when you use the UV Mapping command all the edges will be already Marked for cut and finish with Continue-Unfold or;
b) Select the object and use the context menu UV Mapping and in the UV Segmenting window mark the edges like you did, Selection-Invert and use the context menu Mark edges for cut and finish with Continue-Unfold.

Try this approach.