Optical trapping is a well-established technique to manipulate and levitate micro- and nanoscale particles and droplets. However, optical traps for single aerosol studies are most often limited to trapping spherical nonabsorbing droplets, and a universal optical trap for the stable confinement of particles regardless of their absorption strength and morphology is not established. Instead, new opportunities arise from levitating droplets using electrodynamic traps. Here, using a combined electrodynamic linear quadrupole trap and a cavity ring-down spectrometer, we demonstrate that it is possible to trap single droplets and simultaneously measure their extinction cross sections and elastic scattering phase functions over extended periods of time. To test the novel setup, we evaluated the evaporation of 1,2,6-hexanetriol under low-humidity conditions, and the evolution of aqueous (NH4)2SO4 and NaCl droplets experiencing changing environmental conditions. Our studies extended beyond spherical droplets and we measured particle extinction cross sections after the efflorescence (crystallization) of the inorganic salt particles. Comparison of measured cross sections for crystallized particles with light scattering model predictions (using Mie theory or the T-matrix/extended boundary-condition method (EBCM) implementations for random orientation, with either the spheroid or superellipsoid parameterizations) enables information on particle shape to be inferred. Specifically, we find that cross sections for dry (NH4)2SO4 particles are accounted for by Mie theory and, thus, particle shape is represented well by a sphere. Conversely, the cross sections for dry NaCl particles are only reconciled with light scattering models pertaining to nonspherical shapes. These results will have implications for accurate remote sensing retrievals of dry salt optical properties and for parameterizations implemented in radiative forcing calculations with changing humidity. Moreover, our new platform for precise and accurate measurement of optical properties of micron-scale and sub-micron particles has potential applications in a range of areas of atmospheric science, such as precise light scattering measurements for ice crystals and mineral dust. It represents a promising step toward accurate characterizations of optical properties for nonspherical and light-absorbing aerosols.