HRTEM pictures should give you the thickness: the nanoparticles centres are less absorbing than the edges (the electrons actually have to go through more material at the edges than at the centre, therefore more absorption at the edges of the nanoparticles).Hence the edges will show up quite clearly if aggregates are not on top of one another; that is if your samples are well taken .
Dynamic light scattering (DLS). Split the sample into two, leave the first batch as cores and form a core/shell using the second batch. Measure the hydrodynamic diameter of each using DLS. The change in hydrodynamic diameter will allow you to estimate the thickness of the shell. The data will also provide you with a size distribution allowing you to determine if the samples are monodisperse or polydisperse. Another advantage of DLS is identifying the presence of thin shells in core/shell materials where the core and shell exhibit similar lattice fringes making it hard to distinguish between the two via TEM . A disadvantage of DLS is it doesn't tell you if you have incomplete shell formation.