Subtract of two STL files in Slic3r software
Given my limited familiarity with all the CAD tools that exist, I would fall back to something that I know does binary operations on volumes -- openScad.

One can create two objects, one from each of the two STL files, and subtract one from the other.  One can also compute intersections, unions, and other operations.

There are probably other programs that also do this, but openScad allows for doing in programmatically, so that once you have it right, you can update the objects without needing to redo the finicky part of the operations.

slic3r may do this, but I haven't seen such features in my multi-year use of slic3r for slicing.  

When in doubt, IMO it is better to script something.  It is virtually never that I do something only once, especially in 3D printing where rapid prototype leads to rapid change and improvement.