When Tisha B’Ab begins on Mosa’eh Shabbat, one must wait until Shabbat ends before removing his leather shoes. Since no displays of mourning are allowed on Shabbat, one should not remove his leather shoes and wear non-leather shoes until after Shabbat.
When, precisely, should one remove his leather shoes? On a regular Tisha B’Ab, we change our shoes at sundown. However, when Tisha B’Ab falls on Mosa’eh Shabbat, this is not possible, because it is still Shabbat until after sunset.
Hacham Ovadia Yosef ZT"L, as recorded in Yalkut Yosef (p. 275; listen to audio recording for precise citation), writes that, technically speaking, one does not remove his leather shoes until the Hazan says "Barechu" at the beginning of Arbit on Mosa’eh Shabbat. Practically, of course, this is not a viable solution for most of us, as we change into non-leather shoes already at home and walk with them to the synagogue. Hacham Ovadia thus adds that if one changes his shoes at home, this should be done twenty minutes after sundown.
Hacham Ben Sion Abba Shaul (Israel, 1923-1998) proposed a different solution, claiming that one could take off his shoes and put on slippers at home as people often do for comfort, without it appearing as a sign of mourning. Since wearing slippers is something that is ordinarily done, it may be done on Shabbat. This way, one can change into slippers already at sundown without observing mourning practices on Shabbat.
As mentioned, however, Hacham Ovadia rules differently, and maintains that one should change out of his leather shoes twenty minutes after sundown.
Summary: When Tisha B’Ab begins on Mosa’eh Shabbat, one should change out of his leather shoes twenty minutes after sunset, and not earlier.
