I'm still using SW2013, but wouldn't Pack and Go do what you need? You can re-name files as part of the process, and un-check parts that you don't want to copy.
In Windows Explorer, select the assy you want to re-use. Right-Click. Find where is says "SolidWorks". Right-Click that. There you will find Rename, Pack & Go, etc...The things you used to find in SW Explorer. I think this is what you are hoping to find.
Un-check the "include broken references" box at the top.
We've run into this and are trying to find a way to make that box un-checked as the default.
We've got duplicate files all over the place because of this default action.
It was a while before we noticed it, and we constantly re-use assemblies to make similar assemblies.
I'm submitting this as an enhancement request.