Well, we can go with Cap's movie being his backstory. But there are a few changes that we need to make concerning the final act. Red Skull was using the Tesseract at a secret Hydra base with his two lead scientists, Baron Zemo and Arnim Zola, and Baron Strucker, his second-in-command. Tony's father, Howard Stark, learned of this base through intercepting coded transmissions from Hydra. Cap, the Howling Commandos (because Cap was pals with them) and Bucky (he's still alive, since the train mission never happened) attacked the base. They arrived at the lab just in time to see Zemo and Zola calling forth a creature from one of the other Norse realms with the Tesseract. The crew defeated the Hydra troops at the base, but Zemo and Skull escaped. The portal to the realms was still open, and the only way to close it would be to destroy the portal... at the cost of one's own life. Bucky didn't hesitate. Fueled by a burning desire for revenge, Cap pursued the two Hydra leaders onto Red Skull's personal ship. He battled Zemo in the storage bay, causing a heap of the doctor's own Chemical X to pour onto him. Cap couldn't waste any more time, so he headed to the bridge. There he found the Red Skull, and battled him. Skull accidentally touched the Tesseract with his bare hands, which seemingly killed him. From there, Cap crashed into the arctic ocean with the Tesseract. The ship was practically an atomic warhead, so he had to dip it into the waters to save the USA. The story needs to be this way for plot purposes, as at least one of the villains I mentioned will be reappearing.
BTW, Cap wouldn't have fought Batroc or Crossbones yet. So they shouldn't be on the Rogues' Gallery.
Otherwise... APPROVED!