I may be missing something blindingly obvious here but, if the account is closed, why would you care if anybody got the cheque forms. And, if the account is open, why are you throwing the cheque forms away? Surely you might use them at some point in the future?
Do cheque forms in the US come with a “use-by” date?
That’s what bandsaws are for. Works a treat. Caveat: DO NOT attempt to cut up checks on a tablesaw!
When I worked for a printing company that printed checks all the samples had a hole punched in the signature line. I was told that this made the machine that read the MICR number spit it out, and unless it was found to be a certified check was considered void. A drill should do the trick.