I'm exactly the same. I'm very left handed, but swing a club right-handed. My brother-in-law (who happens to play a lot more squash than he does golf) is right handed, and reckons that he feels like his golf swing is a double-handed forehand. (the power and control come mainly from his right hand). I reckon that my power and control (what there is of it) comes from my left hand.

I have no idea what the conventional wisdom is, but I know if I swing left-handed it looks like a cow giving birth to a roll of barbed wire.