halacha - Is a person allowed to wear tefillin during Tish'a B'Av Shacaharit if he won't be able to daven mincha that day?

Let's say a person needs surgery on Tish'a B'Av in the afternoon. He knows that he will not be able to daven Mincha.

Should he wear tefillin during Shacharit instead? What if he attends shul for Shacahrit where no one else will be wearing tefillin? Would that cause problems such as mar'it ayin? If that's not OK, should he daven in shul without the tefillin, then when he returns home, put them on?