In this paper and in Paper I (this issue), we analyse and interpret the near-infrared observations of a complete hard X-ray selected sample of AGN, mainly optically classified as Seyfert 1 s. The data are presented in Paper 1, in which we decompose the radial surface brightness profiles into a point source, bulge and disc components. In this paper we use the derived non-stellar/stellar fractions to subtract the stellar contribution present in small nuclear apertures. We examine the evidence for the presence of an underlying non-thermal power law, modified by dust reddening, as the origin of the non-stellar near-infrared component. We find a correlation between the hard X-ray and near-infrared luminosities. This correlation does not, however, improve following the subtraction of the stellar component, as might be expected if there is an underlying power law connecting the two regions. Objects with steep near-infrared spectra are reddened and dominated by thermal emission from hot dust, whereas sources with flatter continua are mainly non-thermal. There is a weak or null correlation between the near-infrared spectral shape and reddening parameters. Some possible explanations for this are discussed. We conclude that the near-infrared continua of most Seyfert 1 galaxies are dominated by non-stellar components. Possible origins are hot dust emission, or a non-thermal component, which could be more important in the high-luminosity sources.