We investigate the electromagnetic interaction of a relativistic stellar wind with small bodies in orbit around the star. Based on our work on the theory of Alfvén wings to relativistic winds presented in a companion paper, we estimate the force exerted by the associated current system on orbiting bodies and evaluate the resulting orbital drift. This Alfvénic structure is found to have no significant influence on planets or smaller bodies orbiting a millisecond pulsar. On the timescale of millions of years, it can however affect the orbit of bodies with a diameter of 100 kilometres around standard pulsars with a period $P \sim $1 s and a magnetic field $B \sim 10^{8}$ T. Kilometer-sized bodies experience drastic orbital changes on a timescale of $10^4$ years.