Judging from the way bandits use throwing knives, while they do prioritize using that attack over using normal melee attacks, changing bows to a special attack weapon and giving it a cooldown would cause the AI to have their units continually close the range, which negates the advantage they should be getting from using a bow in the first place. I suspect that you could instead include an initiative penalty on the bow, or cause the use of the bow to cost an extra turn, and that would allow the AI to make use of the bows without constantly closing the range (I think).
Another possible issue, if you make bows a special attack with a range limitation, is that the AI will first close to within proper usage range, and then end their turn, and then on their next turn make use of the special attack, at least judging from how bandits use throwing knives.
You would also not really have a distinct archer model, if you turn bows into a special attack option, as I don't think that any accessory affects the unit model, although I suppose you could go for making a secondary weapon slot that provides some change to the model.
Having the cooldown also might not directly relate to the current relative strengths of bows, since the number of turns that you 'lose' by using a bow rather than a melee weapon varies by the total initiative of the unit.