Note that Winamp cannot play certain DRM protected WMA content even with the official WMA plugin that coems with Winamp.
Another alternative is record the music as it plays. Setup a recording application such as Goldwave and prepare a blank 44kHz, 16-bit stereo track. Bring up the soundcard's recording audio mixer, mute all devices except 'wave' and max the 'wave' level.
Finally press record in Goldwave (or other recording tool) and press play in Windows Media player. Allow the track to play through, then press stop in Goldwave, cut-out the excess silence at the start & end of the track and save your track. Do a test play to be sure it recorded fine
Even if the soundcard does happen to add a slight hiss to the recorded track, this is nothing compared to the audible artefacts present in WMA.