This paper describes the use of an optical vortex trap for the transport and fusion of single femtoliter-volume aqueous droplets. Individual droplets were generated by emulsifying water in acetophenone with SPAN 80 surfactant. We demonstrate the ability of optical vortex traps to position trapped droplets precisely while excluding surrounding aqueous droplets from entering the trap, thereby preventing unwanted cross contamination by other nearby droplets. Additionally, the limitation of optical vortex traps for inducing droplet fusion is illustrated, and a remedy is provided through modulation of the spatial intensity profile of the optical vortex beam. Spatial modulation was achieved by translating the computer-generated hologram (CGH) with respect to the input Gaussian beam, thereby shifting the location of the embedded phase singularity (dark core) within the optical vortex beam. We present both simulated and experimentally measured intensity profiles of the vortex beam caused by translation of the CGH. We further describe the use of this technique to achieve controlled and facile fusion of two aqueous droplets.