I agree with Roy that the linearity of coils wound on powdered iron
cores is unlikely to be a problem for you. A while back, I had
occasion to question if some filters we use, made with small powdered
iron toroid core inductors, were causing distortion, so I built up some
similar filters with air-core coils and very good capacitors that I
knew would not distort. The result was "no change". That corresponds
in this case to third order intercepts in excess of +50dBm, which would
be considered at least pretty good by all but the fanatics for use in
receivers. I don't know how much in excess of +50dB, because that was
about the limit of what I could see in that test. Also, I know that
the broadband transformers used in the best H-mode mixers have allowed
those mixers to perform at similarly high--and higher--third order
intercepts. I suppose those transformers are transmission-line types,
wound on ferrite cores.

Cheers,
Tom