Is it possible to create a gadget that will allow an agent to select wrap up reasons from a list that will change depending on the skill group?
No, Finesse doesn't have the a relationship between wrap up reasons and skill groups. Also, the reason codes are loaded one time when the agent logs in. Even if the list of reason codes (whether it is not ready, logout or wrap up) changes after the agent is logged in, the list will not change on the agent desktop. The agents won't see this change until they refresh their browser.
Finesse only has the ability to have a different reason code list per team.