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Yeah, the general implementation concept I'm thinking of going with for option 2 will use a few helper functions:
url, coerced_to_str = _coerce_to_str(url)
if coerced_to_str:
 param = _force_to_str(param) # as appropriate
...
return _undo_coercion(result, coerced_to_str)
The first helper function standardises the typecheck, the second one complains if it is given something that is already a string.
The last one just standardises the check to see if the coercion needs to be undone, and actually undoing the coercion.