Keyed woodwinds are almost invariably right-handed. Renaissance instruments with one key for the bottom little finger (like tenor recorders) were sometimes made with the key forked so that either hand could be at the bottom, and if the lowest hole was unkeyed, sometimes two were drilled side by side with the unused one filled with wax.

Cathal McConnell plays a right-handed keyed flute left-handed. He keeps most of the keys shut with chewing gum and rubber bands.

Given the amount of reworking you'd have to do to make a left-handed version of a complex modern woodwind instrument, if any exist they'd cost a fortune. It's not just a matter of reshaping half a dozen pieces of wood, as with a fiddle. Almost every key in a flute, clarinet or sax is asymmetric, and needs to be made on an asymmetric jig.