I wouldn't bother waiting for it to dry out, cement will take better to a damp surface.
As above, prise out all the loose stuff with an old screwdriver (or better still a thin masonry chisel) and then repoint with may be a 4:1* soft sand / cement. (add a drop of washing up liquid to the mix, it will make it more workable)
*those bricks look quite soft so may be a weaker mix ?
By the looks of the wall you won't make it look any worse, and you may give it another decade before a proper job needs done.