Torsional motions are ubiquitous in the solar atmosphere. In this work, we perform three-dimensional (3D) numerical simulations that mimic a vortex-type photospheric driver with a Gaussian spatial profile. This driver is implemented to excite magnetohydrodynamic waves in an axially symmetric, 3D magnetic flux tube embedded in a realistic solar atmosphere. The Gaussian width of the driver is varied, and the resulting perturbations are compared. Velocity vectors were decomposed into parallel, perpendicular, and azimuthal components with respect to pre-defined magnetic flux surfaces. These components correspond broadly to the fast, slow, and Alfvén modes, respectively. From these velocities, the corresponding wave energy fluxes are calculated, allowing us to estimate the contribution of each mode to the energy flux. For the narrowest driver (0.15 Mm), the parallel component accounts for  per cent of the flux. This contribution increases smoothly with driver width up to nearly 90 per cent for the widest driver (0.35 Mm). The relative importance of the perpendicular and azimuthal components decreases at similar rates. The azimuthal energy flux varied between ∼35 per cent for the narrowest driver and  per cent for the widest one. Similarly, the perpendicular flux was  per cent. We also demonstrate that the fast mode corresponds to the sausage wave in our simulations. Our results, therefore, show that the fast sausage wave is easily excited by this driver and that it carries the majority of the energy transported. For this vortex-type driver, the Alfvén wave does not contribute a significant amount of energy.