Hypothesis A on vanishing shadow volume for Euclidean obstacles

Let $K\subset\mathbb E^n$ be a smooth manifold of codimension at least $2$ with a regular embedding, and let $\mathcal W(\epsilon)$ denote the volume of the trapping locus $\mathsf{Trap}(SN_\epsilon)$ associated with the obstacle $K$. Hypothesis A. For all sufficiently small $\epsilon>0$, $\mathcal W(\epsilon)=0$. This concerns whether the trapping locus has zero volume for sufficiently small tubular neighborhoods of any such Euclidean obstacle. The supplied text gives no resolution beyond stating the hypothesis.