My understanding of Skippy is that you just pick him up in the ally; use him for 50 take-downs; then he'll switch to the opposite setting; when that happens the quest to return him to his owner is triggered (but don't have to do it).
I don't know anything about Skippy and killing mecha? But hum... to answer the question... I found police-star alerts that have militech involved generally have mecha. There are also some random places out in the badlands with a few mecha. You could farm the guards (mecha) at Kerry's House?
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As a note: you can also attach a PAX mod to skippy to make him non-lethal.
I think it'll switch modes (headshot / bullet in the knee) after 50 kills regardless of enemy types, and then trigger the quest after another 50 kills.