Welcome to the Official Redemption® Message Board!
Cards that are exchanged are considered "owned" by the player who has possession of them. At least that's the way the exchange with Seven Wicked Spirits was ruled. I don't see why Stalks would be any different. You should be able to set aside a Hero that you received with Stalks.
One interesting thing I find about the past discussions is that Bubbleboy has always agreed with the ruling. Suddenly he "hates" Redemption because of it.