We propose here a multiscale strategy based on continuous solvent Brownian dynamics (BD) simulations to study the dynamical properties of aqueous suspensions of charged nanoparticles. We extend our previous coarse-graining strategy [V. Dahirel et al., J. Chem. Phys. 126, 114108 (2007)] to account for hydrodynamic interactions between solute particles. Within this new procedure, two BD simulations are performed: (1) The first one investigates the time scales of the counterions and coions (the microions) with only one nanoparticle in the simulation box but explicit microions, (ii) the second one investigates the larger time scale of the nanoparticles with numerous nanoparticles in the simulation box but implicit microions. We show how individual and collective transport coefficients can be computed from this two-scale procedure. To ensure the validity of our procedure, we compute the transport coefficients of a 10-1 model electrolyte in aqueous solution with a 1-1 added salt. We do a systematic comparison between the results obtained within the new procedure and those obtained with explicit BD simulations of the complete system containing several nanoparticles and explicit microions. The agreement between the two methods is found to be excellent: Even if the new procedure is much faster than explicit simulations, it allows us to compute transport coefficients with a good precision. Moreover, one step of our procedure also allows us to compute the individual transport coefficients relative to the microions (self-diffusion coefficients and electrophoretic mobility).