The influence of in-plane and canted magnetic fields on spin spirals and skyrmions in atomic bilayer islands of palladium and iron on an Ir(111) substrate is investigated by scanning tunneling microscopy at low temperatures. It is shown that the spin spiral propagation direction is determined by the island's border which can be explained by equilibrium state calculations on a triangular lattice. We find a different response of spin spirals to in-plane magnetic fields for a propagation direction parallel to the applied field as compared to perpendicular, which originates from their cycloidal nature. As a result, the spin spiral propagation direction may be reorientated by in-plane fields. Furthermore, it is demonstrated that also skyrmions are distorted in canted fields which allows to determine the sense of magnetization rotation as enforced by the interfacial Dzyaloshinskii-Moriya interaction.