The search for new relatively easy physicochemical methods for the structural identification of carbon nanotubes represents a key challenge. Here, analyzing the experimental data on double-walled carbon nanotubes (DWCNTs) obtained by us and taken from the literature, we have expressed the magnitude of elastic coupling between two tubular walls forming a DWCNT as a simple function dependent not only on DWCNT diameters but also on the difference between the chirality angles of the constituent nanotubes. To get this quite unexpected result, which allows us to relate more precisely the structural parameters of a DWCNT with frequencies of its radial breathing-like modes (RBLM), we have developed a new model for the RBLM dynamics that takes into account a possible deposition of water molecules from ambient air onto the DWCNT surface. The model constructed allows us to predict the higher prevalence of DWCNTs comprising two walls with identical handedness. The application of the results obtained for the identification of DWCNTs is also considered.