Solar geoengineering refers to a range of proposed methods for counteracting global warming by artificially reducing sunlight at Earth's surface. The most widely known solar geoengineering proposal is stratospheric aerosol injection (SAI), which has impacts analogous to those from volcanic eruptions. Observations following major volcanic eruptions indicate that aerosol enhancements confined to a single hemisphere effectively modulate North Atlantic tropical cyclone (TC) activity in the following years. Here we investigate the effects of both single-hemisphere and global SAI scenarios on North Atlantic TC activity using the HadGEM2-ES general circulation model and various TC identification methods. We show that a robust result from all of the methods is that SAI applied to the southern hemisphere would enhance TC frequency relative to a global SAI application, and vice versa for SAI in the northern hemisphere. Our results reemphasise concerns regarding regional geoengineering and should motivate policymakers to regulate large-scale unilateral geoengineering deployments.