The safest thing to do with cash before a move is usually to have less of it lying around. A bank deposit the week before beats any packing technique for anything you are not actively spending on moving day.
Pro tip: Depositing cash before the move is simpler and safer than any packing method; only carry what you actually expect to spend during the move itself.
Watch out: Cash and small valuables forgotten in old hiding spots like coat pockets or book pages are commonly lost permanently during a move.