Well this looks liek a bit of fun. Let's see...
I think he works best when he operates as a middle man, a fence and information broker rather than a mobster in his own right. The Iceberg Lounge can do double duty as a legitimate front for his black market deals as well as a Casablanca type neutral ground for competing mobsters. Doesn't need to be deformed, just a short, portly guy that got his name for his preference for black tie formal wear and an almost snobbish sense of vanity. Likes to think of himself as a cultured intellectual and prides himself on his blue blood background (the the old Cobblepot fortune has long since dried up.)
Easy in this day and age. He's a crazed, shut-in blogger turned predatory serial killer with a thing for puzzles. He's smart enough to be able to show off his handy work while protecting his identity, but can't resist leaving clues. Imagine something along the lines of the Zodiac killer with an internet connection.
Very little adaptation needed with Selina, just so long as the costume is a tasteful mix of style (she is a "cat" after all) and practicality. The full body jumpsuit actually makes a lot of sense when you consider that she wouldn't want to leave behind fingerprints, fibres or even DNA at the scene of the crime.
Botanist turned eco-terrorist with a thing for honey traps and exotic poisons with no known antidotes. Probably targeting Bruce's industrialist buddies (or Wayne Enterprises in general) for their involment in oil spills, logging, pesticides and toxic waste dumping. A genuinely stunning beauty who uses her looks to get close to powerful men and dose them with a slow acting contact poison.
As others have said, the BTAS take is pretty much the definitive version in terms of his characterisation. It's just a matter of making the cryonic stuff halfway plausible (as plausible as sonar phones and memory cloth at least.)
Huge meat-head, possibly ex-military/special forces (perhaps discharged for violent misconduct and general psychotic behaviour?) Maybe joined up to escape a childhood in the circus as a sideshow attraction (do those things still even exist?), maybe has a scale like skin condition. Probably heavily into body modification, filed teeth, split tongue, implants under the skin, facial tattoos, that kind of thing. Basically hired muscle but with a mean streak about a mile wide and a really sick and creative taste for pain also makes him very sought after as an underworld "interrogator".
As with Catwoman and Freeze; if it ain't broke, don't fix it! Just giver her more of a gothy/punk/Priss from Blade Runner look and it's job done.
Lucha libre type wrestler and steroid freak turned Mexican drug cartel enforcer. Did some time in some of the southern hemisphere's least pleasant correctional facilities. Maybe a qualified pharmacologist before he fell on hard times and venom is his own personal cocktail of steroids, amphetamine and growth hormones. A nasty brew that maintains his physique and fuels his berserker rage but has made his body so dependent on it, he can never stop taking it or else he'll go into terminal withdrawal. Much smarter than he looks and went from hired goon to running a cabal by systematically killing his way up the food chain while keeping his competitors at each other's throats.