Our molecular dynamics (MD) simulations have shown that nanodroplets containing water and nonane are nonspherical and strongly phase-separated. This "Russian doll" structure may be simply but realistically modeled as a spherical nonane lens that partially wets a spherical water droplet. We call this the lens-on-sphere model. Here, we present an analytical calculation of the particle form factor, P(q), needed to analyze the intensity curves for small-angle neutron and X-ray scattering by aerosol particles with this type of structure. For this model, the particle form factor must be evaluated by numerical integration. In addition, an exact formulation of the particle form factor is presented for cylindrically symmetric droplets with otherwise arbitrary position-dependent scattering length density. This result enables direct calculation of P(q) from numerical MD simulation data. Results using both formulations are compared, and excellent agreement is found between them. Analytical results are also presented for two limiting cases of the general result: the sphere-on-sphere model and the sphere-in-sphere (SIS) model, corresponding to contact angles of 180 degrees and 0 degrees, respectively. Finally, a generalization of the SIS model to ellipsoidal droplets is given.