We investigate the long-term evolution of an initially buoyant magnetic flux tube emerging into a gravitationally stratified coronal hole environment and report on the resulting oscillations and outflows. We perform 2.5-dimensional nonlinear numerical simulations, generalizing the models of McLaughlin et al. and Murray et al. We find that the physical mechanism of oscillatory reconnection naturally generates quasi-periodic vertical outflows, with a transverse/swaying aspect. The vertical outflows consist of both a periodic aspect and evidence of a positively directed flow. The speed of the vertical outflow (20-60 km/s) is comparable to those reported in the observational literature. We also perform a parametric study varying the magnetic strength of the buoyant flux tube and find a range of associated periodicities: 1.75-3.5 minutes. Thus, the mechanism of oscillatory reconnection may provide a physical explanation to some of the high-speed, quasi-periodic, transverse outflows/jets recently reported by a multitude of authors and instruments.