Left-handed pianos do exist.
I would even think being left-handed would improve your technique over a right-handed pianist, generally speaking. Right-handed pianists (or pianists-to-be) tend to neglect their left hand an awful lot, and they can get away with it in most cases.
What is a left-handed piano? How is one of those different from a right-handed piano? With guitars, you can put the strings on upside down and get a left-handed guitar, but I cannot imagine how you could construct a left-handed piano... unless the high pitched notes are on the left and the low ones on the right???