Compact groups of galaxies provide insight into the role of low-mass, dense environments in galaxy evolution because the low velocity dispersions and close proximity of galaxy members result in frequent interactions that take place over extended time-scales. We expand the census of star formation in compact group galaxies by Tzanavaris et al. (2010, Cat. J/ApJS/212/9) and collaborators with Swift UVOT, Spitzer IRAC and MIPS 24{mu}m photometry of a sample of 183 galaxies in 46 compact groups. After correcting luminosities for the contribution from old stellar populations, we estimate the dust-unobscured star formation rate (SFR_UV_) using the UVOT uvw2 photometry. Similarly, we use the MIPS 24 {mu}m photometry to estimate the component of the SFR that is obscured by dust (SFR_IR_). We find that galaxies which are MIR-active (MIR-'red'), also have bluer UV colours, higher specific SFRs, and tend to lie in HI-rich groups, while galaxies that are MIR-inactive (MIR-'blue') have redder UV colours, lower specific SFRs, and tend to lie in HI-poor groups. We find the SFRs to be continuously distributed with a peak at about 1M_{sun}_/yr, indicating this might be the most common value in compact groups. In contrast, the specific SFR distribution is bimodal, and there is a clear distinction between star-forming and quiescent galaxies. Overall, our results suggest that the specific SFR is the best tracer of gas depletion and galaxy evolution in compact groups.