I think the nacelle and exhaust cone do affect the contrail formation in some way, what is the relationship between them? Do the famous 787 Chevrons also affect the contrails? And How does it compare with engines with exhaust mixer?
Ultimately the engine is dumping water into the atmosphere and this will quickly cool to ambient temperature. Depending on the relative humidity at altitude it may or may not condense. These factors are irrespective of the engine design provided that combustion is more or less complete, so the only factor that will significantly affect contrail formation is the extent to which the exhaust gases are distributed. This will certainly be affected by the design but is hard to predict in general how; it’s mostly down to fluid dynamics well downstream of the engine itself.