Modern usage has freighted it heavily with antisemitism. It's a dog-whistle for those motherfuckers. Don't use it.

Etymology
US, 1992. Variant of sleazy, possibly influenced by sketchy (“dubious, unnerving”); alternatively analyzed as blend of sketchy and sleazy.

Note that "skeevy" comes from Italian, or so says my super-Sicilian friend. When she and her cousins would come in from playing outside her grandmother would tell them they were "schiffiati", or filthy. "Skeevy" come from the same word.

I always thought "skeezy" was a mashup of "skanky" and "sleazy"

The word you're looking for is "portmanteau".

You actually use "shyster" in regular conversation?

Do you also constantly talk about getting "gypped"?

Easy E said it best:
"Then I take the other pussy, put it the freezer. Then I always have an on-hold skeezer."

Thank you for getting thus song stuck in my head

Definitely not skanky, it's sketchy and sleazy.