The higher derivative gravity includes corrections of the second order in curvature and allows for both Schwarzschild and non-Schwarzschild asymptotically flat black-hole solutions. Here, we find the grey-body factors and energy emission rates for Hawking radiation of test Dirac and electromagnetic fields in the vicinity of such a non-Schwarzschild black hole. The temperature and mass of the black hole monotonically decrease from their Schwarzschild values to zero when the coupling constant is increased up to its extremal value. Nevertheless, for small and moderate values of the coupling constant, the Hawking radiation is enhanced, and only in the regime of large coupling it is suppressed, as one could expect. The reason for such counterintuitive behavior is the important role of the grey-body factors: for small and moderate couplings, the temperature falls relatively slowly, while the effective potentials for black holes of the same mass become considerably lower, allowing for much higher transmission rates. We have also estimated the lifetime of such black holes and shown that the range of black-hole masses at which ultrarelativistic emission of massive electrons and positrons starts is shifted towards smaller black-hole masses when the coupling constant is large.