  The discovery of GeV gamma-rays from classical novae indicates that shocks
and relativistic particle acceleration are energetically key in these events.
Further evidence for shocks comes from thermal keV X-ray emission and an early
peak in the radio light curve on a timescale of months with a brightness
temperature which is too high to result from freely expanding photo-ionized
gas. Paper I developed a one dimensional model for the thermal emission from
nova shocks. This work concluded that the shock-powered radio peak cannot be
thermal if line cooling operates in the post-shock gas at the rate determined
by collisional ionization equilibrium. Here we extend this calculation to
include non-thermal synchrotron emission. Applying our model to three classical
novae, we constrain the amplification of the magnetic field $\epsilon_B$ and
the efficiency $\epsilon_e$ of accelerating relativistic electrons of
characteristic Lorentz factor $\gamma \sim 100$. If the shocks are radiative
(low velocity $v_{\rm sh} \lesssim 1000$ km s$^{-1}$) and cover a large solid
angle of the nova outflow, as likely characterize those producing gamma-rays,
then values of $\epsilon_e \sim 0.01-0.1$ are required to achieve the peak
radio brightness for $\epsilon_B = 10^{-2}$. Such high efficiencies exclude
secondary pairs from pion decay as the source of the radio-emitting particles,
instead favoring the direct acceleration of electrons at the shock. If the
radio-emitting shocks are instead adiabatic (high velocity), as likely
characterize those responsible for the thermal X-rays, then much higher
brightness temperatures are possible, allowing the radio-emitting shocks to
cover a smaller outflow solid angle.
