Well, depending on the range of notes you need to play, and how much you need to close the filter on the noise, technically you can't really filter a sine wave, since it contains no upper harmonics. So, theoretically, you could filter the noise and the sine wave together, with little consequence to the actual sine tone.
Otherwise, I would just pick the colour of noise that works best, modulate its level independently in conjunction with the filter, in whatever ratio gets you close to the effect you're looking for.
You could also try using noise to modulate the filter cut-off directly, controlled by an envelope or LFO.
Cheers!