Click & Collect can override any shipping method of your choice to display the carrier select dropdown; in the Click & Collect Settings -> Pickup In Store Options Display Name filed of the app, enter the name of the shipping method you want to override in the checkout.
In this way, you can use Click & Collect alongside advanced carrier managers such as ShipperHQ; create a customer shipping method in your carrier manager and match its name with the value in Click & Collect Settings->Pickup In Store Options Display Name (or vice-versa) to connect the two.