You can wash the roots of the plants and leave the plant (completely naked, unpotted) for several days to completely dry off. I know several people who do that (some who read this forum) but I've always been too afraid. But you can remove the vast majority of old soil this way.
I would not use a pre-made mix for cacti. All of them are too high in organic material, even the ones which say they're designed for cacti.
I would take either a mix like that, or coir/peat and mix it with 50% pumice, 50% perilite, or 50% chicken grit. The soil ideally needs to be VERY chunky and contain much less actual "soil" than many people realize.
I posted this thread a couple weeks ago and some of the comments directly address what you're asking about:
The thread "Brands of peat-free soil or soil mixes" in
Cactus and Succulents forum