  Aims: Our aim is to study the presence and properties of small-scale swirls
in numerical simulations of the atmospheres of cool main-sequence stars. Our
particular focus is on understanding the variations in these properties for
different stellar types and their sensitivity to the surface magnetic field.
Furthermore, we aim to investigate the role of these events in the energy
transport within the simulated atmospheres.
  Methods: We analyze three-dimensional, radiative-magnetohydrodynamic,
box-in-a-star, numerical simulations of four main-sequence stars of spectral
types K8V, K2V, G2V, and F5V. These simulations include a surface small-scale
dynamo responsible for amplifying an initially weak magnetic field. Thus, we
can study models characterized by very weak, or, magnetic fields in near
equipartition. To identify small-scale vortices in horizontal layers of the
simulations, we employ the automated algorithm SWIRL.
  Results: Small-scale swirls are abundant in the simulated atmospheres of all
the investigated cool stars. The characteristics of these events appear to be
influenced by the main properties of the stellar models and by the strength of
the surface magnetic field. In addition, we identify signatures of torsional
Alfv\'enic pulses associated with these swirls, which are responsible for a
significant vertical Poynting flux in the simulated stellar photospheres.
Notably, this flux is particularly significant in the K8V model, suggesting a
possible link to the enhanced basal \ion{Ca}{ii} H and K fluxes observed in the
range of $B-V$ color index $1.1 \leq B - V \leq 1.4$. Finally, we present a
simple analytical model, along with an accompanying scaling relation, to
explain a peculiar result of the statistical analysis that the rotational
period of surface vortices increases with the effective temperature of the
stellar model.
