the only problem with using the cane on the side you have trouble on is that when you take a step forward your weight is all on the injured side. by using the cane on the opposite side you have 2 points of contact with the ground supporting your weight more evenly and allowing you to step rather than hop.
hugs and prayers
bring on the bubblewrap
before you cut !!! see if your p.t dept at your local hosp will measure just for you so it's correct. you sure don't want my bad advice to ruin your good cane