I'm pretty sure the 1/4" plug you are using on the mixer is made for that kind of signal.
If i recall correctly, you shouldn't need a balanced input (via direct box) unless before you get to the mixer you have long lengths of unbalanced cords running parallel and near large power sources or big magnets. These can impart loits of noise into an unbalanced line that could be avoided in a balanced one.
That said, when recording bass, i need to turn off the monitor to my computer to avoid an unpleasant buzz that comes through the lines, but that originates from the Bass itself or the cord from head that acts as preamp, since i have a balance signal going from the output of the head to the mixer i use. if you had somehting similiar a direct box might help, but it would probabaly be easier and cheaper to sort out the stuff and move away fromt he interfering equipment.
Daav