I had one just like that where I caught a big old cardón (Pachycereus pringlei) with an unprotected hand, without thinking of course. The spines on that plant are actually pretty stout, but they're also really sharp, so they still went way into my hand and broke off there, leaving me to nurse my wounds for some time afterward.
That was when I decided that plant was big and heavy and hazardous enough to merit its own set of wheels on the patio, so I can move it freely without impaling myself any more than necessary.
As for repotting big barrels, my preferred technique is lots of towels or rugs or whatever kind of thick fabric might be lying around. Our dog used to lay on a thick old bath mat with a rubberized pad and that was just about perfect. Wrap a couple (starting high enough up on the stem that you can see the base of the plant afterward, if you lift the towel a bit) and test for prickliness, then wrap a couple more if you need to, until you can actually grab onto and handle the plant based on the fabric that's tangled up between its spines.
In the end you are lifting it by the spines, but because there's so many of them caught up in the towels, they distribute the weight quite nicely, and don't tend to do much damage to the towels or bathmat in the end.
