Though he had been hitting as a lefty throughout his career, on August 7, 1893, New York Giants first baseman Roger Connor stepped up to the plate right-handed for the first time against a left-handed Brooklyn Bridegrooms pitcher. The right side of the plate turned out to be lucky for Connor that day, as he belted two homers and a single en route to a 10-3 win.
I did a small bit of poking around regarding Connor’s switch-hitting, and while specific details seem hard to find, I notice that some sites have him listed as a left-handed hitter while others list him as a switch-hitter. A case can be made either way, it seems.