I use PCManFM to delet files from my USB thumb drives. I mount the drive and open it with PCManFM. In PCManFM > Edit > Preferences, uncheck Move deleted files to "trash bin." This activates the "delete forever" function. I then delete the files I need to, unmount the drive and remove it. Then rest the trash.
To check that the files are gone, remount the drive, open it and have a look.
Of course formatting the drive twice will remove all the files on it and make them irrecoverable.