I have a few questions: how is that you're sure that the noise is coming from the windings? What kind of noise is it?
I'm a bit at a loss as to how windings can make noise. There are no moving parts in the windings. The windings form part of the rotar which is attached to shaft and the whole thing spins. I would have thought that any would be coming from the brushes or the entire rotar assembly, ie. the shaft, rattling back and forth because it's missing a washer or a shim. Alternatively, I suppose the brushes could be rattling inside the brush housings or if a brush is worn down enough, the spring that the brush is attached to is scraping on the commutator.
If it's the latter, then if you use the motor you might ruin it.