Searches for optical transients are usually performed with a cadence of days to weeks, optimised for supernova discovery. The optical fast transient sky is still largely unexplored, with only a few surveys to date having placed meaningful constraints on the detection of extragalactic transients evolving at sub-hour timescales. Here, we present the results of deep searches for dim, minute-timescale extragalactic fast transients using the Dark Energy Camera, a core facility of our all-wavelength and all-messenger Deeper, Wider, Faster programme. We used continuous 20 s exposures to systematically probe timescales down to 1.17 minutes at magnitude limits g > 23 (AB), detecting hundreds of transient and variable sources. Nine candidates passed our strict criteria on duration and non-stellarity, all of which could be classified as flare stars based on deep multi-band imaging. Searches for fast radio burst and gamma-ray counterparts during simultaneous multi-facility observations yielded no counterparts to the optical transients. Also, no long-term variability was detected with pre-imaging and follow-up observations using the SkyMapper optical telescope. We place upper limits for minute-timescale fast optical transient rates for a range of depths and timescales. Finally, we demonstrate that optical g-band light curve behaviour alone cannot discriminate between confirmed extragalactic fast transients such as prompt GRB flashes and Galactic stellar flares.