Ultra-compact X-ray binaries (UCXBs) are a subclass of low-mass X-ray binaries (LMXBs) characterised by tight orbits and hydrogen-poor donor stars. We present a spectral and timing study in the hard X-ray band of 11 of the 20 confirmed UCXBs, based on 37 archival NuSTAR observations. Using both X-ray colours and fractional root mean square values, we show that our sample spans the hard, soft, and intermediate X-ray states. Subsequently, we performed an X-ray spectral analysis using, when data allowed, the three-component model ─ an approach increasingly adopted for neutron star LMXBs. This work represents the largest LMXB sample analysed to date with this methodology. We focus on the properties of the X-ray continuum and report typical values for each X-ray state. Overall, UCXBs exhibit similar spectral properties to their longer-period counterparts, suggesting no major differences in the innermost regions of X-ray binaries regardless of disc size or chemical composition. A possible exception is found in the soft-state sample, which shows Comptonisation fractions higher than those typically observed in regular LMXBs, although the statistics remain limited. Finally, we discuss the case of the slow X-ray pulsar 4U 1626─67, where we report the discovery of a very cold hard state with an electron temperature of ∼6 keV ─ comparable to those usually observed in soft states of neutron-star LMXBs.