By shaker, do you mean a powered sub? If so, then either it would have a built in crossover, so you could use a full-range out, or it wouldn't, and you could just take out the speaker and switch the wires going to it, or use a modified signal cable. On the other hand, if it has a built in crossover, it may be out of phase already, so you could use the lowpass out with no problem. Or, the builders could have had the forethought to reverse the phase for you, in which case....
(falls out of chair)
You sound like a competent individual. Experiment, and let us know how it turns out!