CPtCrl

You would use the expression "Southpaw"!

The origins of the term goes divides neatly into the halves, one for each part of the word;

One’s dukes or dooks are one’s hands, of course, as in the American to duke it out, to fight with the fists. There are two stories about its origin, both of which take it back to London slang of the early to middle part of the nineteenth century. One theory is that an older slang term for the hand was fork, in reference to using the fingers like a pair of tweezers to slip something surreptitiously out of a person’s pocket without them knowing about it. Cockney rhyming slang then converted fork into Duke of York and so, by the usual process of abbreviation, to duke. Some authorities regard this as an over-complex evolution, and suggest that the word is really from Romany, the language of the Rom, or gypsies, in which dukker means to tell fortunes, presumably by palmistry. This theory is itself less than totally convincing.
The other half of the term, molly, seems to be yet another example of the use of that word to mean an effeminate male, as in mollycoddle. The implication seems to have been that anybody left-handed was a bit queer in at least one respect.
There are various spellings for the slang term, including molly-duker, and there’s also a related form, molly-hander. It’s first recorded in Australia in the 1920s.