What you're describing is artificial, player-imposed restrictions. That's no different than speed runs or any other challenge players have decided to set for themselves. Without the game imposing restrictions (less effectiveness with weapons your character is unskilled in), the difference is largely meaningless. At least when we're discussing what your character can do. What they will do is another question, one more about preferences and personality than hard restrictions.
The fact that you can either use this or that at one time is a big restriction.
As for which one you're going to use more, there's where the roleplaying will take part