Sorry about the damage done to your plant, but that is an "occupational hazard" for all of us with plant collections.
A plant's future depends on the health of its rootball, not the appearance of its foliage. So long term you have nothing to be concerned about, although I see no reason to move an otherwise thriving plant to a larger pot. Larger pots don't heal physical damage, but they do disrupt the roots and the watering routine you have been using. Be very careful you do not inadvertently over-water now that there is an abundance of soil to retain water for a long time.
There is no reason to leave damaged foliage on any plant. Once damaged or discolored, foliage never recovers, so remove it for aesthetic reasons. Most plants, including Rattail Cacti, benefit from regular pruning even when they have not been damaged. Pruning is not something to be feared or avoided. Pruning will not affect the health of a plant, but it will affect its appearance. So prune it back so that it looks better. Also, understand that new growth will emerge on stems just below where you make the pruning cuts. Thus, you control where new growth comes in and how your plant will look in the future. Be bold and prune back as much as you can stand!