If you took oral medications called anti-androgens such as spironolactone or androcur, they would reduce your body hair after a very long time. But at the same time you would lose muscle tone and possibly become sterile and impotent.
The medications would definitely reduce your strength, which as a competitive athlete would eliminate you from competition.
Birth control pills generally contain some estrogen and some progesterone but not anti-androgens. Some are too weak to have much of a feminizing effect, but some types are strong enough. I think that they would cause you to have secondary female characteristics over time such as breast growth or fat deposits. They say that progesterone has a bit of a masculinizing effect, so that may increase hair growth.
James is right that you would need to remove the hair with electrolysis if you want to remain a competitive swimmer.