The feedpoint choke will help keep unbalance currents from flowing on the outside of the coax, which is helpful. Being a conductor in the presence of an electromagnetic field, currents may be induced on the coax by radiation from the antenna. This effect will be more pronounced if the coax runs close to the antenna, if it runs parallel to the polarization of the radiation or if the length the coax resonates at the operating frequency. Since currents flow on the radials, they are part of the radiating system and can induce currents on the feedline, so the same effects apply.
You can minimize the induced currents on the outside of the coax shield by winding turns of the coax through ferrite toroids - 31 material should be a good choice - at spacings that avoid half wavelengths on the bands you operate. This has two benefits: 1) it prevents the outside of the coax shield from behaving like a half-wave dipole, which would experience maximum induced current; 2) it puts the high choking reactances at lower-impedance points on the shield, where it can be proportionally more effective.
Brown, K9YC, has published a lot of useful information on techniques, materials and turns required.