Piano wire is available at many hobby shops. I think the smallest starts at 0.002" and goes up well past 0.125". The drill bit might be a bit stiffer because it is hardened.
Our world does not revolve around fractional drill sizes. If you need an assortment of coil-winding diameters, buy a cheap number drill set from one of those tool outlets like Harbor Freight. Those Chinese imports aren't worth a darn as drill bits, but they will give you some diameters from which to choose for winding coils.