Hayes Nine Hydro brakes - oil do you think that I could use Shimano mineral oil on/in Hayes Nine Hydro brakes (where it says Dot 4).

Thanks for your help people!
No. Can not, must not. Fluid type mismatches in either direction can make seals and other non-metal parts degrade, swell, and/or fail. Mineral oil, being the less caustic and reactive one, will generally do it more gradually when this mistake does get made, but it still does it or at least can.