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Abstract Supermassive black holes (SMBHs) are thought to be located at the centers of most galactic nuclei. When galaxies merge, they form SMBH binary (SMBHB) systems, and these central SMBHs will also merge at later times, producing gravitational waves. Because galaxy mergers are likely gas-rich environments, SMBHBs are also potential sources of electromagnetic (EM) radiation. The EM signatures depend on gas dynamics, orbital dynamics, and radiation processes. The gas dynamics are governed by general-relativistic magnetohydrodynamics (MHD) in a time-dependent spacetime. Numerically solving the MHD equations for a time-dependent binary spacetime is computationally expensive. Therefore, it is challenging to conduct a full exploration of the parameter space of these systems and the resulting EM signatures. We have developed an analytical accretion-disk model for the mini-disks of an SMBHB system and produced images and light curves using a general-relativistic ray-tracing code and a superimposed harmonic binary BH metric. This analytical model greatly reduces the time and computational resources needed to explore these systems, while incorporating some key information from simulations. We present a parameter-space exploration of the SMBHB system, in which we study the dependence of the EM signatures on the spins of the BHs, the mass ratio, the accretion rate, the viewing angle, and the initial binary separation. Additionally, we study how the commonly used fast-light approximation affects the EM signatures and evaluate its validity in general-relativistic MHD simulations.