Alternate Terms 

Alternate terms for this type of story can be taken from the terms sometimes used for these puns.  In particular "groaner", see Wiktionary (definition 3), or "screamer", from the reader's reaction at the end. Since many people have never run across one of the Ferdinand Feghoot stories, they would not know "feghoot". The only one of them I have read was definitely a pun, but seemed rather flat on first reading, not in either the groaner or screamer categories.
agb