The circumgalactic medium (CGM) is a crucial component of galaxy evolution, but thus far its physical properties are highly unconstrained. As of yet, no cosmological simulation has reached convergence when it comes to constraining the cold and dense gas fraction of the CGM. Such components are also challenging to observe directly, as they require sub-millimetre (sub-mm) instruments with a high sensitivity to extended and mostly diffuse emission. We present a state-of-the-art theoretical effort at modelling the [CII] 158 μm, [CI](1−0) 609 μm, [CI](2−1) 370 μm, CO(3−2) 867 μm, and [OIII] 88 μm line emissions that arise from the interstellar medium (ISM) and CGM of galaxies, with the goal of studying the contribution from different cold (T < 104 K) components of galaxy halos. We used the high-resolution cosmological zoom-in simulation PONOS (mgas = 883.4 M⊙), which represents a typical star-forming galaxy system at z = 6.5, composed of a main disc with stellar mass M* = 2 × 109 M⊙ that is undergoing a major merger. We adopted different modelling approaches based on the photoionisation code CLOUDY. Our fiducial model uses radiative transfer post-processing with RAMSES-RT and KROME (KRAMSES-RT) to create more realistic far-ultraviolet (FUV) radiation fields, which we then compared to other sub-grid modelling approaches adopted in the literature. We find significant differences in the luminosity and in the contribution of different gas phases and galaxy components between the different modelling approaches. [CII] is the least model-dependant gas tracer, while [CI](1−0) and CO(3−2) are very model-sensitive. In all models, we find a significant contribution to the emission of [CII] (up to ∼10%) and [OIII] (up to ∼21%) from the CGM. Our fiducial global radiative transfer (RT) model produces a lower density, T ∼ 104 K tail of [CII] emission that is not seen in the other more simplistic models and that resides entirely in the CGM, ionised by the FUV background and producing the extended halos observed in [CII] at high-z. Notably, [CII] and [OIII] trace different regions of the CGM: [CII] arises from an accreting filament and from the tidal tails connecting the main disc and its merging satellites, while [OIII] traces a puffy halo surrounding the main disc, probably linked to supernova feedback. We discuss our results in the context of sub-mm observations. Using simulated spectra and mock maps, we show that, despite the rather compact angular extent of PONOS’s CGM, deep ALMA observations would not detect this component, even in [CII] which is the brightest available tracer. Instead, a next generation single-dish observatory such as the Atacama Large Aperture Submillimeter Telescope (AtLAST) could detect PONOS’ CGM in [CII] at a high signal-to-noise ratio, and possibly even in [OIII].