I looked at the implementation in Lib/_pyio.py.  The only way to change the error handler is by calling TextIOWrapper.reconfigure() and supply the new error handler as the "errors" parameter.  For example:

>>> import io
>>> s = io.TextIOWrapper(io.BytesIO())
>>> print(s.errors)
strict
>>> s.reconfigure(errors='replace')
>>> print(s.errors)
replace
>>>