We perform simulations to study the hydrodynamics of a conical-shaped swimming micro-robot that ejects catalytically produced bubbles from its inside. We underline the nontrivial dependency of the swimming velocity on the bubble deformability and on the geometry of the swimmer. We identify three distinct phases during the bubble evolution: immediately after nucleation the bubble is spherical and its inflation barely affects the swimming speed; then the bubble starts to deform due to the confinement gradient generating a force that propels the swimmer; while in the last phase, the bubble exits the cone, resulting in an increase in the swimmer velocity. Our results shed light on the fundamental hydrodynamics of the propulsion of catalytic conical swimmers and may help to improve the efficiency of these micro-machines.