Sándor Szalay was a figure skater for the BKE club. Between 1926 and 1932 he competed with Olga Orgonista in pairs. In 1928, they won the first Hungarian championship in pairs, a feat they repeated for the next two years. They became the first European champions in pairs at the 1930 European Championships in Vienna and defended their European title in 1931 in St. Moritz. When they were third at the Budapest World Championships in 1929, they won the first World Figure Skating Championship medal for Hungary. Two years later, they finished second behind Emília Rotter and László Szollás. At the 1932 Lake Placid Winter Olympics, they again finished behind the Rotter-Szollás duo but this time they missed out on the medals in fourth place.
After Olga Orgonista married after the 1932 Olympics, the pair broke up and Szalay stopped being an active sportsman.
He did not break away from figure skating even after finishing his competitive career, as he worked as a judge for years. After the second World War, as the new president of the Hungarian Skating Association and BKE, he played an active role to restore the ice rink in Budapest. He also worked as a construction contractor and, after World War II, as a construction inspector for the National Rubber Industry Company.