Optically levitated and cooled nanoparticles are a new quantum system whose application to the creation of non-classical states of motion and quantum sensing is fundamentally limited by recoil heating. Here we study the creation of stable 3D optical traps using optical cylindrically polarized vortex beams with radial and azimuthal polarization. We find that a significant reduction in recoil heating by up to an order of magnitude can be achieved when compared to conventional single Gaussian beam tweezers. We show that these beams allow trapping of larger particles outside the Rayleigh regime using both bright and dark tweezer trapping. By controlling the wavelength of the trapping laser, or the size of the particles, nonlinear and repulsive potentials of interest for the creation of non-classical states of motion can also be created