Shibuya's cobordism conjecture for self Delta-equivalence

Let oriented links be related by self $\Delta$-equivalence when one can be transformed into the other by self delta moves and ambient isotopies, where each self delta move has all three strings belonging to the same link component. Two oriented links are cobordant if they cobound disjoint unions of properly embedded surfaces in $S^3\times[0,1]$. Shibuya's conjecture. Any two cobordant oriented links are self $\Delta$-equivalent. This conjecture concerns the relationship between link cobordism and self Delta-equivalence; the source presents it as a conjecture, and no resolution is given in the supplied text.