The process p(G + W* -y + x + livy t-x is calculated to O ( a , ) for general CP-conserving WWy couplings. At the Fermilab Tevatron center-of-mass energy, the QCD corrections to Wy production are modest, and the Born and incllisive O(a,) cross sections have similar sensitivities to the effects of anomalous couplings. At supercollider energies, the inclusive QCD corrections are large at high photon transverse momenta, reducing the sensitivity to nonstandard WWy couplings by up to a factor 2. The size of the QCD corrections can be reduced significantly, and a large fraction of the sensitivity lost can be regained, if a jet veto is imposed. PACS nunlber(s): 13.85.Qk, 12.38.I3x, 14.80.Er