I'm not entirely certain what you're trying to say here. If you're asking "if a vesparan's ovum is fertilised by a non-vesparan's sperm, does the resulting child have non-vesparan traits?", I'd say they should, assuming no dominant/recessive breeding shenanigans are involved; that's just how hybrids work. If you're asking "if an egg that is 100% vesparan is incubated inside a non-vesparan, does the resulting child have non-vesparan traits?", I'm pretty sure the answer's no; the incubator isn't passing on any genetic material to the eggs they're incubating.
However, I don't know for certain that both of these are the case; they're just the most likely answers IMO, and the non-zero possibility I'm wrong is why I suggested Azzy get a cock rather than Liaden. If it was the other way around, then in the case I'm wrong it's most likely their children will be more Azzy than Liaden (at least on the genetic level); having Azzy impregnate Liaden would probably get around that. If I'm right, the only thing that would make it matter which one gets the cock is that one case would involve the extra step of Azzy having to oviposit the egg(s) into someone, probably Liaden (for obvious reasons).