I think Win ME may have the "smooth edges of screen fonts" feature too, but I am not sure. You would need to check in: Display Properties (right-click desktop) - "Appearance" Tab - "Effects" button - Second check box labelled "Use the following method to smooth edges of screen fonts". If it's ticked then untick that second checkbox then OK then OK again and try mIRC.
NOTE: Aside from that the font cannot be changed in the switchbar buttons in any version of Windows. If Win ME doesn't have what I described above then I am not sure what might be causing your problem.