A widely accepted explanation for the origin of the ubiquitous small-scale magnetic field observed on the solar surface is the presence of a small-scale dynamo (SSD) operating in the sub-surface layers of the Sun. To shed light on the functioning of this SSD, a number of numerical studies of a realistic solar atmosphere have been carried out in the past two decades, greatly improving our knowledge on how an SSD operates. Nevertheless, virtually no studies focused on SSD action on the surface of other main-sequence stars. This motivates the work reported here. Hydro and magneto-hydrodynamics simulations of a small partial volume encompassing the surface layers of F5V, G2V, K2V, and K8V main-sequence stars are carried out with the radiative magnetohydrodynamic CO5BOLD code, investigating how SSD action can amplify a tiny seed magnetic field. In particular, the growth rate of the magnetic to kinetic energy ratio is characterized in terms of the Reynolds and magnetic Reynolds numbers of the simulations, and of the effective temperature and surface gravity of each star. It is found that the small-scale dynamo operating in the K2V simulation is the fastest in amplifying the magnetic energy among the four cases considered here. However, similar saturation values of the magnetic to kinetic energy ratio, of about 1%, are found at the surface for all the four stars. Ultimately, we investigate the spatial structure of the magnetic field resulting from SSD action and how it interacts with the plasma in the stellar atmospheres.