Lovely plant you have there! I see it seems there are more than one in there, good for a repot, but I will not use vermiculite, it holds water. If you have no pumice then just add some more perlite in the cactus mix you will use. Just remember also to empty that saucer under the pot once water drains out so it will not sit in water.
Those leaves are really fun and easy to root, lay them on the cactus mix in a part shade area and it should grow new roots or new little leaves first.
Love BC! It rains more often in BC, so you really have to make the media very well draining, since your present container is plastic, so it takes awhile longer for media to dry vs. clay containers which easily absorbs water away, so there is faster drying time.
Have fun!