Aim does have some parts that are conscious and some parts that are subconscious, replicating what you do subconsciously is possible consciously and if you are able to do it either way, you will improve your muscle memory's ability to do it both ways. The idea is that you are always more consistent when your conscious focus is fixated upon the target and what's happening in-game rather than what's happening in real life, because you begin to use the mouse to control things on screen more like how you would something in real life, rather than focusing on moving what's in your hand in arbitrary ways to match a moving thing you see on-screen.
When it comes to the issue that you are having, it's best to focus on the game and let your subconscious mind take over the manner in which you grip your mouse, because while your grip most definitely affects your ability to aim and the space which you have to maneuver called your range of motion (ROM), it's very difficult as a human to make effective and meaningful changes to your grip that would BOTH allow further ROM while also keeping a tight enough grip that your mouse doesn't just meaninglessly slip around in your hand. So, let your brain do its thing with the grip, don't think about that part and just play the game as best you can.