The constant emergence of SARS-CoV-2 resistance drives the search for new antivirals. We screened the SARS-CoV-2 cysteine proteases, the main protease (Mpro) and papain-like protease (PLpro), with 141 peptidyl and peptidomimetic inhibitors designed to target a trypanosome cysteine protease. Five compounds (1a-5a) inhibited Mpro (IC50 of 0.1601-16.42 µM), whereas none inhibited PLpro. Compounds 1a-4a inhibited human cathepsin L (hCatL; 0.184-10.74 µM), which is important for viral entry into human cells. Compounds 1a and 5a, and its synthesised (R,S) enantiomer, 5b, which share a benzyl carbamate moiety, inhibited the Mpro of SARS-CoV/MERS-CoV (0.0732-0.8295 µM). The three compounds were biochemically characterised as covalent reversible inhibitors. Compounds 5a and 5b, which contain vinyl ketone warheads, were specific for Mpro, and this behaviour was supported by covalent and noncovalent computational simulations. This study highlights the importance of revisiting legacy assets to identify starting points for new antiviral drugs.