Recent work has shown that type-1 superconductors may undergo genuine wetting or interface delocalization transitions. These transitions arise when superconductivity is enhanced at the surface or at an internal defect plane. Experimental verification of the effects associated with these wetting transitions is possible and has to some extent already been achieved in twinning-plane superconductors, such as Sn. Here we derive an expression for the wall/superconductor interfacial tension Γ W / S C , valid when the Ginzburg-Landau parameter κ is small. This expression is essential in locating the low-κ interface delocalization phase boundary accurately, and thus allows us to complement the previous numerical results for the wetting phase diagram. We find that the phase boundary is singular in the limit κ → 0, in the parabolic manner κα(τ-τ * ) 2 , where τ = ζ/b is the ratio of the bulk coherence length to the surface extrapolation length. We furthermore calculate the superconducting order parameter and vector potential profiles and verify numerically that the low-κ expansion provides an accurate approximation across a broad range of κ values.