In this paper we present the approach we have used to determine and account for the anisoplanatic point spread function (PSF) in deep adaptive optics (AO) images for the Survey of a Wide Area with NACO (SWAN) at the ESO VLT. The survey comprises adaptive optics observations in the Ks band totaling ~ 30 arcmin^2, assembled from 42 discrete fields centered on different bright stars suitable for AO guiding. We develop a parametric model of the PSF variations across the field of view in order to build an accurate model PSF for every galaxy detected in each of the fields. We show that this approach is particularly convenient, as it uses only easily available data and makes no uncertain assumptions about the stability of the isoplanatic angle during any given night. The model was tested using simulated galaxy profiles to check its performance in terms of recovering the correct morphological parameters; we find that the results are reliable up to Ks ~ 20.5 (K_AB ~ 22.3) in a typical SWAN field. Finally, the model obtained was used to derive the first results from five SWAN fields, and to obtain the AO morphology of 55 galaxies brighter than Ks = 20. These preliminary results demonstrate the unique power of AO observations to derive the details of faint galaxy morphologies and to study galaxy evolution. ; Comment: 12 pages, 12 figures. Accepted for publication in A&A