Cosmological constraints from galaxy clusters rely on accurate measurements of the mass and internal structure of clusters. An important source of systematic uncertainty in cluster mass and structure measurements is the secure selection of background galaxies that are gravitationally lensed by clusters. This issue has been shown to be particular severe for faint blue galaxies. We therefore explore the selection of faint blue background galaxies, by reference to photometric redshift catalogs derived from the COSMOS survey and our own observations of massive galaxy clusters at z~0.2. We show that methods relying on photometric redshifts of galaxies in/behind clusters based on observations through five filters, and on deep 30-band COSMOS photometric redshifts are both inadequate to identify safely faint blue background galaxies. This is due to the small number of filters used by the former, and absence of massive galaxy clusters at redshifts of interest in the latter. We therefore develop a pragmatic method to combine both sets of photometric redshifts to select a population of blue galaxies based purely on photometric analysis. This sample yields stacked weak-lensing results consistent with our previously published results based on red galaxies. We also show that the stacked clustercentric number density profile of these faint blue galaxies is consistent with expectations from consideration of the lens magnification signal of the clusters. Indeed, the observed number density of blue background galaxies changes by ~10-30 per cent across the radial range over which other surveys assume it to be flat.