A bronze wire wheel operated by a power tool would be unnecessarily harsh. If the wire is the same as wire on a bronze bristle brush used to clean bores, then I suggest using one of the above fine wools with oil and gentle hand power.
I've used 0000 steel wool on wood stocks during final refinishing. This used with Tru-Oil does a fantastic job of sprucing up old stocks. The last statement does not apply to refinishing--just cleaning up a stock.
Being ham fisted, I learned to avoid power tools when working on guns. So called gunsmiths mess up plenty with Dremel tools even though they don't view themselves as bubba's.