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Long and short gamma-ray bursts are traditionally associated with galactic environments, where circumburst densities are small or moderate (few to hundreds of protons per cubic cm). However, both are also expected to occur in the disks of Active Galactic Nuclei, where the ambient medium density can be much larger. In this work we study, via semi-analytical methods, the propagation of the GRB outflow, its interaction with the external material, and the ensuing prompt radiation. In particular, we focus on the case in which the external shock develops early in the evolution, at a radius that is smaller than the internal shock one. We find that bursts in such high density environments are likely characterized by a single, long emission episode that is due to the superposition of individual pulses, with a characteristic hard to soft evolution irrespective of the light curve luminosity. While multi-pulse light curves are not impossible, they would require the central engine to go dormant for a long time before re-igniting. In addition, short GRB engines would produce bursts with prompt duration that would exceed the canonical 2 s separation threshold and would likely be incorrectly classified as long events, even though they would not be accompanied by a simultaneous supernova. Finally, these events have a large dynamical efficiency which would produce a bright prompt emission followed by a somewhat dim afterglow.