When you're ready to re-pot, just use two or three old compost bags in an empty pot , place it on the top and turn the whole thing on its side, take the old pot away , balancing the plant and rootball on its side, remove loose compost dead roots ect. move the new slitely bigger pot with some new mix in the bottom and turn the plant right side up into it's new home. Fill around the edge. Top dress to your own taste. Hey Presto
Sometimes it is good to re-pot a cactus when you acquire it, as some come in a mix of nearly pure peat or fine sand ect. How they are meant to grow , I've no idea.
Now re potting a ten foot terscheckii is another mater entirely and might need some scaffolding.
Also big opuntias are very unforgiving.
Lash the beast to an aluminium ladder, with suitable padding on the rungs, and the pot below the lowest rung. Then lower it down onto a sack barrow, finding the balance point. You can then tip it, move it, do what you like with it. Of course you then have to get it upright again but a few strong backs will sort that out.