Someone suggested to us last year to use this tool made I think for dog grooming. It looks like a flexible double sided saw and you can use it hooked together or take it apart and drag it across your steer to get the dead hair out. Works great, and the steers love it. My son used it on his steer last year, and when he would try to quit using it and walk out of the pen, the steer would follow and nudge him , wanting him to keep doing it. It got to be pretty comical to watch ;D...lol
I think you can get them at most farm or pet supply stores, and they are around 7-$10.