A cross-layer design in the presence of an underlying indeterminacy of propagation channels and interference levels is formulated for wireless cognitive networks, where the nodes are allowed to perform network coding. In lieu of full inter-system cooperation, statistics of signal-to-noise-plus- interference ratios (SINRs) and interference levels are leveraged to obtain optimal end-to-end session rates, network code design variables, and transmit-powers, while sharing spectral resources with incumbent primary systems in an underlay setup. Solution of the formulated optimization problem is hard to approach, mostly because of a lack of tractability of the resultant SINR distributions. Nonetheless, suitable approximations are employed to obtain an approximate convex problem, amenable to efficient solution. Numerical tests verify the ability of the proposed scheme to adapt network and physical layer parameters to the propagation environment.