NOx forms in reducing regions at much lower concentrations than in oxidizing regions, all else being equal. Non-premixed flames are more likely to forms such regions and therefore suppress NOx formation. However, for the same reasons, they promote soot formation. It is not clear exactly what configuration of honeycomb you have in mind, but honeycombs find use as flame stabilization systems, flow straighteners, mixing inhibitors, and temperature control, all of which could affect NO production.
Thermal NOx formation is dependent on local temperatures, local oxygen supply and residence times. Whether a non-premixed combustion process produces less thermal NOx than a premixed combustion, is dependent on these factors, and hence the flow field in which the combustion takes place. Near stoichiometric premixed combustion often tends to produce more NOx than a non-premixed combustion process at similar operational conditions, but this is not always the case. You really need to look into the details of your flow field and chemistry. Of course, if you burn a fuel with nitrogen compounds (oil, coal, some biogases), things are entirely different.
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