I never expected to have to use machine guns one day as I try to do a zero-kills run so I have to start to develop that weapon line but yeah, it sounds like a solution. Damn the skulls.
FWIW, going lethal on the Skulls is encouraged since you're not penalized for doing so. Especially for that variant, since their armor requires those kinds of weapons to deplete. What you would get penalized for is killing the puppet soldiers that are around, but as long as you're marking, you should be able to keep track of them, especially since they're so slow.