Molecular channel exploration perseveres to be the prominent solution for eliciting structure and accessibility of active site and other internal spaces of macromolecules. The volume and silhouette characterization of these channels provides answers for the issues of substrate access and ligand swapping between the obscured active site and the exterior of the protein. Histone deacetylases (HDACs) are metal-dependent enzymes that are involved in the cell growth, cell cycle regulation, and progression, and their deregulations have been linked with different types of cancers. Hence HDACs, especially the class I family, are widely recognized as the important cancer targets, and the characterizations of their structures and functions have been of special interest in cancer drug discovery. The class I HDACs are known to possess two different protein channels, an 11 Å and a 14 Å (named channels A and B1, respectively), of which the former is a ligand or substrate occupying tunnel that leads to the buried active site zinc ion and the latter is speculated to be involved in product release. In this work, we have carried out random acceleration molecular dynamics (RAMD) simulations coupled with the classical molecular dynamics to explore the release of the ligand, N-(2-aminophenyl) benzamide (LLX) from the active sites of the recently solved X-ray crystal structure of HDAC2 and the computationally modeled HDAC1 proteins. The RAMD simulations identified significant structural and dynamic features of the HDAC channels, especially the key 'gate-keeping' amino acid residues that control these channels and the ligand release events. Further, this study identified a novel and unique channel B2, a subchannel from channel B1, in the HDAC1 protein structure. The roles of water molecules in the LLX release from the HDAC1 and HDAC2 enzymes are also discussed. Such structural and dynamic properties of the HDAC protein channels that govern the ligand escape reactions will provide further mechanistic insights into the HDAC enzymes, which, in the long run, have a potential to bring new ideas for developing more promising HDAC inhibitors as well as extend our atomic level understandings on their mechanisms of action.