Dean, yes, you could spray any number of things on the surface and slow the cleanup but that will only mask a problem which should be repaired to protect your home. The mortar is losing it's adhesion from age, and probably from some moisture in the joints. If you spray it to keep it off the floor, it will still be breaking down right there in the wall, and eventually you have stones separated by loose sand. Then it will be a problem, as the weight of the structure and outside moisture will push out the sand.
Have the joints tuck-pointed and make sure there is adequate drainage away from the home. This is especially important with a mortared stone basement!