I do not think using a ledge for recharging the attack cooldown was intended, otherwise, you would recharge instantly to remove that boring pause you have to do.
I'm planning to add a special attack for when you press attack on the ledge so player have more choice of movements but this will have to do for now
Also planned to add something that run slowly after the player to force player to keep moving forward so any lost time on the ledge or any obstacle would be crucial!