Shilykovsky competed internationally from 1956 to 1960, and took part in two Winter Olympics, both times in the 10,000 m. His best season was 1958, when he won the overall silver medal in both the European Championships at Eskilstuna and in the World Championships at Helsinki, on both occasions trailing just behind Oleg Goncharenko.
Shilykovsky's international career spanned from 1956 to 1960, with notable appearances in two Winter Olympics, each time competing in the 10,000 m. His most successful year was 1958, when he secured a silver medal overall at both the European Championships and World Championships, finishing narrowly behind Oleg Goncharenko.