Q. When someone has to visit a family sick person during Tisha Beav morning, can one wish him a Refuah Shleima or is that prohibited since it may be seen as a prohibited salutation on that day?

A. Kovetz Halochos (p. 421) permits wishing a Refuah Shleima when visiting the ill.
Horav Kalman Ochs Shlit’a maintains that Refuah Shleima is not a form of greeting.
One may instead just recite aloud a Tefila for the ill and it could be even be more appreciated than just saying Refuah Shleima. One has to daven for the ill when visiting as it is an integral part of the mitzva of Bikur Cholim
Horav Shlomo Miller’s Shlit’a opinion is similar.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller, Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu and Horav Kalman Ochs Shlit’a