After you have completed the procedure for deregistration of your old hanko, you should shave the surface of the old hanko so that it can no longer be used before discarding it. It is recommended that you register your new hanko at the same time as the procedure for deregistration of your seal, so that you will not be in a hurry later.
Bank seals should also be disposed of in the same manner as above, with the seal face scraped off after completing the procedures for discontinuing the registration of the seal registered with the bank.