A weakly interacting dark matter candidate is very difficult to detect at highenergy colliders like the LHC, if its mass is close to, or higher than, a TeV. We argue that the pair-annihilation of such particles may give rise to e + e − -pairs in dwarf spheroidal galaxies (dSph), which in turn can lead to radio synchrotron signals that are detectable at the upcoming square kilometre array (SKA) telescope within a fairly moderate observation time. We investigate in detail the underlying mechanisms that make this possible. Both particle physics issues and those pertaining to astrophysics, such as diffusion, electromagnetic energy loss and the effects of interstellar magnetic field, are examined with reference to their roles in generating radio flux. We first identify the detectability criteria in a model-independent manner. It is observed that fluxes may be detectable for scenarios that are consistent with all constraints available till date from γ-ray and cosmic-ray observations. Thereafter, using benchmarks based on popular scenarios involving physics beyond the standard model, we show that it should be possible to detect the radio flux from a dSph like Draco with 100 hours of observation at the SKA, for dark matter particle masses upto 4-8 TeV. The corresponding frequency distributions are also presented, where it is found that the frequency range 300 MHz -50 GHz is especially useful for recording the annihilation signals of trans-TeV particles.