  We construct cobordism maps for the \textit{minus} version of instanton knot
homology associated to a \textit{specially decorated} knot cobordisms of
arbitrary genus between two null-homologous knots in closed oriented
$3$-manifolds. As an application of our construction, we recover an inequality
between the torsion order of knots in instanton theory, which was originally
established in Heegaard Floer theory by work of Juh\'asz, Miller, and Zemke. We
further use this inequality to compute the framed instanton Floer homology of
any non-zero Dehn surgeries along an alternating knot of bridge index at most
$3$.
