Your new cactus friend has its idiosyncrasies (as do our people friends) that we must learn to respect.
Every year or two, your cactus will want some new soil in which to wiggle his or her toes. He or she will probably resist being transplanted, however.
For the protection of your plant, it is wise to use a newspaper or other such item that has been folded many times to produce a strong sling of 3" to 5" width. With the sling wrapped around the protesting cactus, you will not only avoid disfiguring your cactus, either by breaking the spines or cutting into the epidermis, but you will also protect yourself from the prickly spines. This method is especially advantageous with the columnar types.
Remember, with all plants, try to assure that the weight is well balanced on either side of the sling so that the plant does not slip through and fall to the ground.
Another method that can be used, depending on your particular situation, requires a set of vegetable "tongs" that have the "tong" part wrapped heavily with cloth. Using these padded "tongs" will aid you in moving your cactus from pot to pot without damaging the plant.