Abstract: Many gamma-ray bursts (GRBs) have been observed from radio wavelengths, and a few at very high energies (VHEs, >100 GeV). The High Altitude Water Cherenkov (HAWC) gamma-ray observatory is well suited to study transient phenomena at VHEs owing to its large field of view and duty cycle. These features allow for searches of VHE emission and can probe different model assumptions of duration and spectra. In this paper, we use data collected by HAWC between 2014 December and 2020 May to search for emission in the energy range from 80 to 800 GeV coming from a sample of 47 short GRBs that triggered the Fermi, Swift, and Konus satellites during this period. This analysis is optimized to search for delayed and extended VHE emission within the first 20 s of each burst. We find no evidence of VHE emission, either simultaneous or delayed, with respect to the prompt emission. Upper limits (90% confidence level) derived on the GRB fluence are used to constrain the synchrotron self-Compton forward-shock model. Constraints for the interstellar density as low as 10(-2) cm(-3) are obtained when assuming z = 0.3 for bursts with the highest keV fluences such as GRB 170206A and GRB 181222841. Such a low density makes observing VHE emission mainly from the fast-cooling regime challenging.