Woo started his competitive swimming, as a 16-year-old South Korean teenager, at the 1994 Asian Games in Hiroshima, Japan.

He helped the South Koreans earn a silver medal in the 4×200 m freestyle relay with a time of 7:33.61.

[3] At the 1998 Asian Games in Bangkok, Thailand, Woo added a bronze medal to his collection for the South Korean swimming team in the 4×200 m freestyle relay.

He also attempted for his first individual medal in the 400 m freestyle (4:00.66), but missed the podium by 0.22 seconds behind Hong Kong's Mark Kwok.

He held off his rival Kwok by almost half the body length to lead the second heat in a lifetime best of 3:58.31.