The first deep-field observations of the JWST have immediately yielded a surprisingly large number of very high redshift candidates, pushing the frontier of observability well beyond z ≳ 10. We here present a detailed SED-fitting analysis of the 10 gravitationally lensed z ~ 9-16 galaxy candidates detected behind the galaxy cluster SMACS J0723.3-7327 in a previous paper using the BEAGLE tool. Our analysis makes use of dynamical considerations to place limits on the ages of these galaxies and of all three published SL models of the cluster to account for lensing systematics. We find the majority of these galaxies to have relatively low stellar masses $M_{\star }\sim 10^7-10^8\, \mathrm{M}_{\odot }$ and young ages t_age ~ 10-100 Myr but with a few higher mass exceptions ($M_{\star }\sim 10^9\rm{-}10^{10}\, \mathrm{M}_{\odot }$) due to Balmer-break detections at z ~ 9-10. Because of their very blue UV-slopes, down to β ~ -3, all of the galaxies in our sample have extremely low dust attenuations A_V ≲ 0.02. Placing the measured parameters into relation, we find a very shallow M_⋆ - M_UV-slope and high sSFRs above the main sequence of star formation with no significant redshift-evolution in either relation. This is in agreement with the bright UV luminosities measured for these objects and indicates that we are naturally selecting UV-bright galaxies that are undergoing intense star formation at the time they are observed. Finally, we discuss the robustness of our high-redshift galaxy sample regarding low-redshift interlopers and conclude that low-redshift solutions can safely be ruled out for roughly half of the sample, including the highest redshift galaxies at z ~ 12-16. These objects represent compelling targets for spectroscopic follow-up observations with JWST and ALMA.