Should I keep the old litter box nearby?

As cats can be quite finicky, they'll often gravitate to what they're familiar with.  It's important to remove access to old litter boxes so your cat's only choice is to try the new litter.  Sometimes this may result in your cat pooping or urinating outside the box.  While obviously not ideal, your cat will eventually transition to the new litter. If this continues on, you can bring the old litter box back to give your cat a break, and then repeat the process again after a day or two.