The negative-equals-reverse conjecture for Schoenflies balls

Let $\Delta$ be a Schoenflies ball, and let $-\Delta$ denote its complementary Schoenflies ball in $S^4$. Write $\bar\Delta$ for $\Delta$ with the opposite orientation. Negative-equals-reverse conjecture. If $\Delta$ is a Schoenflies ball, then

$$-\Delta=\bar\Delta.$$

Equivalently, $\Delta\times I$ is diffeomorphic to $B^5$. The conjecture concerns whether the complementary and oppositely oriented Schoenflies balls agree, and is a problem in smooth 4- and 5-manifold topology.