Motivated by controversy concerning the origin of alkali metal vapor in the atmosphere of the Jovian satellite Europa, we present laboratory studies of the electron-stimulated desorption (ESD) and photon-stimulated desorption (PSD) of atomic K deposited on the surface of thin water ice films. These ice films of both crystalline and amorphous modifications simulate the surface of icy satellites. A pulsed low-energy electron gun and a mercury arc lamp serve as sources of electron and UV irradiation. X-ray photoelectron spectroscopy (XPS) is used for surface chemical state control. Both ESD and PSD of potassium atoms from ice exhibit appearance thresholds at ∼4 eV, which is more pronounced for the case of crystalline ice than for amorphous ice. The velocity distribution of desorbed K atoms, measured at 100 K, is peaked at ∼500 m/s (by comparison, the peak for Na is at ∼800 m/s), with the high-energy portion extended up to ∼3000 m/s. The mechanism of desorption is identified as an electronically excited charge transfer from ice to alkali ion, followed by desorption. We conclude that along with magnetospheric energetic ion sputtering processes, UV solar photons and electron fluxes with E > 4 eV may cause alkali metal desorption from Europa's surface.