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With the discovery of gravitational waves (GWs), the disks of Active Galactic Nuclei (AGN) have emerged as an interesting environment for hosting a fraction of their sources. AGN disks are conducive to forming both long and short Gamma-Ray Bursts (GRBs), and their anticipated cosmological occurrence within these disks has potential to serve as an independent tool for probing and calibrating the population of stars and compact objects within them, and their contribution to the GW-detected population. In this study, we employ Monte Carlo methods in conjunction with models for GRB electromagnetic emission in extremely dense media to simulate the cosmological occurrence of both long and short GRBs within AGN disks, while also estimating their detectability across a range of wavelengths, from gamma-rays to radio frequencies. {We investigate two extreme scenarios: “undiffused”, in which the radiation escapes without significant scattering (i.e. if the progenitor has excavated a funnel within the disk), and “diffused”, in which the radiation is propagated through the high-density medium, potentially scattered and absorbed. {In the diffused case,} we find that the majority of detectable GRBs are likely to originate from relatively low redshifts, and from the outermost regions of large supermassive black hole (SMBH) masses, . In the undiffused case, we expect a similar trend, but with a considerable contribution from the intermediate regions of lower SMBH masses. Detectable emission is generally expected to be dominant in prompt $\gamma$-rays if diffusion is not dominant, and X-ray afterglow if diffusion is important; however, the nature of the dominant observable signal highly depends on the specific AGN disk model, hence making GRBs in AGN disks also potential probes of the structure of the disks themselves.