To saturate a transistor you typically need 1:10 to 1:20 base current:collector current. So in your case, to switch 75 mA, that would mean 3.75-7.5 mA base current. The data sheet of the particular transistor should have more information.
An EC voltage of 112 mV sounds very low to me, even if saturated. Even at a (very large) 1V drop you'd have only 75 mW of power dissipation so indeed nothing to worry about either way at these low currents.