Your suggestion works, however It looks like i need to tick check for timer when still holding key, because without checking it there is a issue where i did:
Click(for one shot) > Release( for duration less than the cooldown) > Click and hold. And with that combo shooting will not start at all.
So i managed to do this
And the IA_Shoot having Pressed and Released triggers.
And now shooting is perfect working without any of the issues above. One downside is that first and second Branch is ticking for checking the bool and if the timer is still active or not, which maybe is not best solution, however it does not look like a big impact of performance so I think i can stick with it.