The generalized cosmetic crossing conjecture for knots

Let $K\subset S^3$ be a knot, and let $c$ be a crossing of $K$. A crossing is nugatory if its crossing circle bounds a disk in the complement of $K$; a generalized crossing change is a Dehn surgery operation along the crossing circle that changes the crossing by an arbitrary nonzero order. Generalized cosmetic crossing conjecture. If a generalized crossing change on $c$ yields a knot isotopic to $K$, then $c$ is nugatory. This is a generalized form of the cosmetic crossing conjecture, which asks whether a non-nugatory crossing change can preserve the knot type. The source states that the corresponding cosmetic crossing question is open, and gives no resolution of this generalized formulation.