I have been a long time user of Zip disks (not any more, though) and never even contemplated that they may need cleaning. Certainly there was never any indication that cleaning needed doing either in the performance of the drive/disks or any other way.
The zip drive is used by my wife. It appeared to be accessing the disk slower than it had in the past and as she was expecting delivery of a new computer I thought I would get a disk cleaner ordered for her. (grovel points)
The problem has now been cured the wife's computer arrived late yesterday afternoon. The zip drive now works like new. So you good people who replied are correct, 'it didn't need cleaning'. Thank you..Lap..