I had to look this up to see what it was in reference to. I'm not all that good at pop culture.
The idiomatic English phrase smooth criminal does not mean HeSwI' Hab. A HeSwI' Hab might be one with no brow ridges, or one who shaved really well this morning. It's pretty meaningless.
The smooth of the song refers to being so skilled that you get the job done with no complications. It implies a certain coolness factor. I can't think of an equivalent Klingon phrase. The closest we ever get to it in canon is in Star Trek V, where Kirk has just escaped Klaa and Klaa says, with admiration, po'qu' He's good (literally, He's very skilled).
jIQochbe'. It feels as though the sentences were created in English and then translated into Klingon, instead of being made up in Klingon. Instead of sentences that are literal translations of English figurative expressions, I'd like to see mundane English sentences that have the payoff of sounding especially slick in Klingon.
I only ever heard the phrase in the song, and had no idea what the "smooth" referred to - I think it referred to his mannerisms. Now for bonus points, how come this smooth criminal's taking part in First Aid training?