In this study, we present and validate a variation of recently-developed physically motivated sub-grid prescriptions for supernova feedback that account for the unresolved energy-conserving phase of the bubble expansion. Our model builds upon the implementation publicly available in the mesh-less hydrodynamic code GIZMO, and is coupled with the chemistry library KROME. Here, we test it against different setups, to address how it affects the formation/dissociation of molecular hydrogen (H$_2$). First, we explore very idealised conditions, to show that it can accurately reproduce the terminal momentum of the blast-wave independent of resolution. Then, we apply it to a suite of numerical simulations of an isolated Milky Way-like galaxy and compare it with a similar run employing the delayed-cooling sub-grid prescription. We find that the delayed-cooling model, by pressurising ad-hoc the gas, is more effective in suppressing star formation. However, to get this effect, it must maintain the gas warm/hot at densities where it is expected to cool efficiently, artificially changing the thermo-chemical state of the gas, and reducing the H$_2$ abundance even in dense gas. Mechanical feedback, on the other hand, is able to reproduce the H$_2$ column densities without altering the gas thermodynamics, and, at the same time, drives more powerful outflows. However, being less effective in suppressing star formation, it over-predicts the Kennicutt-Schmidt relation by a factor of about 2.5. Finally, we show that the model is consistent at different resolution levels, with only mild differences.
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