I’ve been growing cacti for over 40 years, with a large collection in two greenhouses. Although I don’t grow the taller cereiods, I’m pretty sure yours is Pachycereus pringlei.
To repot, you can wrap the stem in towels, or use two slabs of packing polystyrene if you have it, or folded newspaper in a collar wrapped round the stem, or even a couple of scrubbing brushes with the bristles against the spiny stem. It would probably be easiest to lay it gently on its side, and try to ease it out, you might need to run a knife around the edge of the pot to loosen it.
It appears to be in a terracotta pot, so it might be best to use a slightly larger terracotta pot, you can get shallower half-pots in terracotta. But it doesn’t need to be much bigger - cacti should never be over-potted.
The best potting mix is John Innes number 2 or 3, mixed with horticultural grit - about 50/50. Once repotted, do not water for a couple of weeks to allow the roots to heal. Normally, in a greenhouse, cacti are winter- dormant and receive no water between October and March, but if you are keeping it in a centrally heated room, then modest watering every few weeks or so will probably suffice.
Remember, these plants have evolved to survive drought conditions, and overwatering kills!