This is more of a general philosophy question, I don't think you will find a clear answer in the traditional sources.
Whenever we discuss ideal state or actions, they are limited by our real situation. We can change our situation, and thereby change the ideals we can reach. Consider a very practical application - someone without too much money can invest it well, and then have more money available in the future. So if they ask what is the most intelligent way to budget their money the answer depends a lot on how well they can invest it. If they are confident they can invest it and expect a high return it makes the most sense to plan on spending more in the future, but if they have no idea how to invest they need to plan assuming all they have is what they have at the moment.
The ideal-ideal for Billy is to not engage in the violent behavior, and to learn better ways to handle his personality. The practical-ideal is more likely to be that he should find legitimate outlets for his violence, even if that means being the state executioner (to continue with your example) assuming that he reasonably believes this outlet will free him from unhealthy pressure and open the way him to change in a positive way. The minimal-ideal is to take any legitimate outlet, even if it makes his personality more destructive, as long as he can stay away from illegitimate violence.
The best way to approach this question is not "should I do this or that", but, "what capacities do I have, how can I develop them, and what is the best way for me to accommodate my current personality as I work on developing myself."
What seems like a very negative choice (in the question, being an executioner) may be an excellent choice if it is part of a life-long change and development plan. What seems like the ideal choice - suppressing the violent instincts completely, and not giving them an outlet - is a pretty poor choice if it is not part of a plan.