Poénaru's conjecture on geometric simple connectivity of contractible 4-manifolds

Let $M$ be a compact contractible $4$-manifold whose boundary is a homology sphere. Write $\operatorname{int}(M)$ for its interior, and let g.s.c. denote geometric simple connectivity. Poénaru's conjecture. If $\operatorname{int}(M)$ is g.s.c., then $M$ is also g.s.c. The conjecture concerns whether geometric simple connectivity of the interior forces the corresponding compact $4$-manifold to admit a handle decomposition without $1$-handles. The source notes consequences for the three-dimensional Poincaré conjecture and the smooth Schoenflies conjecture, but gives no resolution.