A solution that works in this specific example and does not require to 
rewire the logic is
to return the printing function inside a record with the right universal 
quantification:

...

type debug = {fn: 'a. ('a, unit, string, unit) format4 -> 'a }[@@unboxed];;

let udebug = {fn=debug}

let give_fn () = Some udebug

...

   | Some {fn} ->
     fn "fn";
     fn "fn param: %s" param