Nontriviality conjecture for the constructed diffeomorphism of the 4-sphere

Let $S_W$ be the Whitney sphere associated to the Whitney disc $W$, and let $\widetilde W$ be a disc with boundary equal to $\partial W$ whose interior is a slight displacement of the interior of $W$, tubed into $S_W$. The pair $(V,\widetilde W)$ determines a pseudo-isotopy of $S^4$ and hence a self-diffeomorphism

$$f\colon S^4\to S^4.$$

Nontriviality conjecture. The diffeomorphism $f$ is not smoothly isotopic to the identity. This would provide a potentially nontrivial pseudo-isotopy of $S^4$ arising from the disc replacement construction. The claim is presented as a potential application and its resolution is not established in the supplied text.