In https://arxiv.org/pdf/2102.04391.pdf, there is an explanation of how one could theoretically use a pair of knots $K$ and $K'$ (one slice and the other not) with the same 0-surgery to generate a counterexample to the 4D Smooth Poincaré Conjecture:
Everything here is in the smooth category. What I was not sure about the argument here is that it seems to be saying that if $W$ were diffeomorphic to $S^4$, then any smoothly embedded 4-ball would be such that $S^4\setminus B^4$ is diffeomorphic to the 4-ball. However, I was wondering, what if we just have a weirdly embedded $B^4$ which makes $S^4\setminus B^4$ not diffeomorphic to the 4-ball? In other words, how do we know that all embeddings of the 4-ball in $S^4$ are isotopic to each other?