One of the writers mentioned in an interview that the invasion would affect Hulkling in a big way.
Isn't the Super Skrull busy with the Phalanx right now? Although according to the last ish of Young Avengers he was busy shipping himself between the Kree and Skrull eimpire in the guise of Teddy.
I'm pretty sure the writers will have no problem figuring out a way around the "All the Skrulls are dead" snag. I mean...how else do you pull of a secret invasion so easily? It's got to be loads easy with everyone thinking your race is pretty much through.
If they're doing a stealthy invasion by replacing key people, I don't see a problem with the majority of their race being extinct. For all we know, this is some fringe group of Skrulls who were sent out covertly and haven't even been in contact with the now-dead empire in years. It's not like all Skrulls magically know where all other Skrulls are at all times.
If anybody engaging in questionable behavior is revealed to be a Skrull, it could be construed as a kind of quick fix. Black Bolt got taken out really easily in World War Hulk, for example, and the revelation that he's a Skrull in New Avengers: Illuminati "fixed" that for a lot of his fans.