If I had a cast on my tefillin arm, how would I wrap tefillin? Would I only do the shel rosh? Or switch hands? (Assuming this is a full-arm cast.)
Rabbi Eli Mansour writes, based on a machlokes involving the Rosh and the Rashba:
Given the difference of opinion in this regard, the Halachic authorities advise a person with a cast on his arm to wear the Tefillin Shel Yad over the cast, but without reciting a Beracha. Instead of reciting the Beracha of “Le’hani’ah Tefillin” over the Tefillin Shel Yad, he should instead recite the Beracha of “Al Misvat Tefillin” over the Tefillin Shel Rosh, having in mind for the Beracha to apply also to the Tefillin Shel Yad.
It should be noted that this entire discussion applies only in a case where the cast cannot be removed and it covers the area where the Tefillin box is worn. Ideally, if possible, one should ask the doctor to apply the cast in a way which allows him to at least wear the Tefillin box on the muscle of the upper arm. If this is not possible, then the Tefillin should be worn over the cast, as discussed.
Summary: If a person has a cast covering the entire arm on which he normally wears Tefillin, and the cast cannot be removed, then he should wear the Tefillin over the cast. In such a case, he recites the Beracha of “Al Misvat Tefillin” over the Tefillin Shel Rosh, and does not recite a Beracha over the Tefillin Shel Yad.
See the linked page for further discussion, and more specific citations.