The only problem with that theory is that we saw Natasha's childhood memories in AoU.
I suppose that would depend on whether Skrull Natasha knows she's a Skrull. After all, the perfect doppelganger sleeper agent is one with all of the memories and personality of the original. Or she was replaced *after* that point in time. Maybe the switch happened during the chaos of the UN bombing?
Either way, the less powerful characters would be the most obvious candidates since you'd have a job explaining how a Skrull can replicate the powers of say Hulk, Vision, Spider-Man, Captain Marvel or Scarlet Witch (at least so long as Marvel can't use Super-Skrulls!

) So Natasha, Clint, Tony, Fury, Maria Hill and the like would be the most likely candidates. Rogers would be up in the air IMO since enhanced strength, speed and agility by human standards probably wouldn't be all that difficult to replicate, but I'm not certain.
I mean sure, they're aliens, anything is possible but from a storytelling perspective it seems more logical that the reason a physically and technologically powerful race like the Kree could be in a prolonged stalemate with a race of shapeshifters is if said shapeshifters were comparatively weak and lacking in resources, making the sneaky shape-shifting their only real advantage. If Skrulls were the physical and technological equals of the Kree Empire then they'd have a clear advantage and would have won aeons ago.
Indeed, one could further extrapolate that the primary reason why the Kree attempted to create Inhuman foot-soldiers is precisely because the Skrulls couldn't replicate exotic abilities and thus couldn't replace them. No infiltrators = Skrull proof.
Yes, the flaw in this plan is that the Kree officers commanding them could be replaced which may be partly why this program was abandoned. Too dangerous. Hell, for all we know a Skrull could have instigated Hive's rebellion in the first place...and been his first meal. I mean he was a shapeshifter of sorts, no?