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