Mod-Cam is a first light and commissioning instrument for the CCAT-prime project's six-meter aperture Fred Young Submillimeter Telescope (FYST), currently under construction at 5600 m on Cerro Chajnantor in Chile's Atacama Desert. Prime-Cam, a first-generation science instrument for FYST, will deliver over ten times greater mapping speed than current and near-term facilities for unprecedented 280-850 GHz broadband and spectroscopic measurements with microwave kinetic inductance detectors (MKIDs). CCAT-prime will address a suite of science goals, from Big Bang cosmology to star formation and galaxy evolution over cosmic time. Mod-Cam deployment on FYST with a 280 GHz instrument module containing MKID arrays is planned for early science observations in 2024. Mod-Cam will be used to test instrument modules for Prime-Cam, which can house up to seven instrument modules. We discuss the design and status of the 0.9 m diameter, 1.8 m long Mod-Cam receiver and 40 cm diameter 280 GHz instrument module, with cold stages at 40 K, 4 K, 1 K, and 100 mK. We also describe the instrument module's cryogenic readout designs to enable the readout of more than 10,000 MKIDs across 18 networks.