Yeah, it's possible. There is an event command that allows you to change an actor's class.
For skills though, you will need to be more creative since skills are assigned by actor, not by class. You can use a script if you want, or the other possibility is to arrange it so that you have multiple repeat actors in the database, each with their own skillsets, and when you choose class you switch your hero to be the one with the skillset for that class.