We revisit the computation of the 1-loop string correction to the “latitude” minimal surface in AdS5 × S5 representing 1/4 BPS Wilson loop in planar N=4 SYM theory previously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of the exact gauge theory result (derived previously from localization) using a different method to compute determinants of 2d string fluctuation operators. We apply perturbation theory in a small parameter (angle of the latitude) corresponding to an expansion near the AdS2 minimal surface representing 1/2 BPS circular Wilson loop. This allows us to compute the corrections to the heat kernels and zeta-functions of the operators in terms of the known heat kernels on AdS2. We apply the same method also to two other examples of Wilson loop surfaces: generalized cusp and k-wound circle.