“Ethically challenged”, “ethically handicapped”, “differently ethicked”, or something else?
I like a simple “unethical” unless you are trying to make it sound like a mental deficiency.
“Ethically challenged”, “ethically handicapped” or “differently ethicked” all sound like you’re making fun of the person. Or, at the very least, insulting them.
Which I’m all for… unless you’re trying to engage in a serious discussion.
And for heaven’s sake, if the less-than-ethical person is in the discussion, I don’t think you’re playing fair if you’re calling someone names like these.
I prefer “left his moral compass in the pocket of his other suit.”
What effect are you looking for?
“Ethically challenged” is a wry understatement. Perhaps the Victorian “is a scoundrel” or perhaps “rogue” would sound classy. Or maybe “makes Bernie Madoff/Jeffrey Skilling look like a saint” if you’re looking for something a bit more glib that shows you pay attention to the news. “Has the ethics of a cockroach-eating wasp” for something with good visuals and just enough snark. Or just “unethical” or “has no ethics” for a flat statement of fact.
Seems like whomever you’re describing is just a plain old fashioned a**hole. That should be good enough. 
Overdrawn at the Ethics Bank
It sounds like you might be feeling out the implications of using phrases that have parallels to descriptions of physical disabilities? I’ve used “ethically challenged” (as someone notes) as wry understatement, but hadn’t really thought about the parallel.
“Their moral compass is perpetually spinning” for humor, I’d say, and straight out “I don’t trust their intentions” for being unethical. Or just ‘unethical’.
“…is a stranger to scruples”
Or “probably thinks “Scruples” is a nightclub”
Well, it was
“Mad, bad, and dangerous to know.” — Lady Caroline Lamb, describing Lord Byron.
Of those three, I’d go with “ethically challenged.” “Handicapped” is usually the word that those two-word constructions are trying to avoid. And “differently ethicked” sounds too much like saying “your bad ethics are just as good as my good ones.”
“Ethically challenged” conveys what I assume is the intended understated tone that you are going for. And, if you’re not going for that, you can just use more direct terms. If you do want to act like people have different ethics, then I’d go with “Your ethics and mine are incompatible” or similar.
Unencumbered by ethical considerations.
A minimally ethically-regulated individual.