  Many gamma-ray bursts (GRBs) have been observed from radio wavelengths, and a
few at very-high energies (VHEs, > 100GeV). The HAWC gamma-ray observatory is
well suited to study transient phenomena at VHEs due 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 December 2014 and May 2020 to search for emission in
the energy range from 80 to 800 GeV coming from a sample 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.
