Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop W in N = 4 SYM theory we work out their 1/N expansions in the limit of large ’t Hooft coupling λ. Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling gs∼g2YM∼λ/N and string tension T∼λ−−√. Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of ⟨W⟩ is a series in g2s/T, the correlator of the Wilson loop with chiral primary operators OJ has expansion in powers of g2s/T2. Like in the case of ⟨W⟩ where these leading terms are known to resum into an exponential of a “one-handle” contribution ∼g2s/T, the leading strong coupling terms in ⟨WOJ⟩ sum up to a simple square root function of g2s/T2. Analogous expansions in powers of g2s/T are found for correlators of several coincident Wilson loops and they again have a simple resummed form. We also find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.