The main reason for toggling is that using the left and right mouse buttons together is physically awkward for the hand.
I do not find it awkward at all
and many games, particularly FPS games, will use both at the same time. But this leads into the next comment.
Plus, by having them independent, it opens up the gameplay to allow shooting while grappling, which doesn’t enhance the gameplay in any meaningful way.
So, don't let someone shoot the gun while the hook is in the air. This is completely independent from the control scheme. This would reduce or maybe eliminate the player actually pressing both mouse buttons at the same time.
The grass just seems greener on the other side, the idea of an independent control scheme is far better than the reality.
Here's where I rant. You can't really tell people what the superior scheme is. I am completely willing to believe that you, personally, prefer a toggle scheme but not that you can tell me what is better for me. For FPS games, I use ESDF instead of WASD so I'm already in the minority there. For DotA-style games instead of skills of QWER, I use ESDF to move the camera instead of the mouse and WRTG for skills. None of these is "far better" than the others.
I fear that if I put in the option to accommodate an independent control scheme, what will happen is that players will have less fun with it, and unwilling to go back to the toggle scheme, will just dismiss the game entirely.
I find this amusing because your existing scheme is half the reason why I 'dismissed' your game as it is.