I would assume circulation is a key to quicker recovery so you would want get into stretching more, massage would probably have its benefits as well. I have no idea about cold showers. I've heard a hot/cold combo does more of a benefit, one after another. Sort of like a hot and cold pack.
However lactic acid causing damage in tissue or stunting muscle growth is an urban myth. The pain you feel after exercise are caused by the micro-tears in muscle fibers in actually. Lactic acid is simply the heat you feel in your muscles whilst you exercise which quickly goes away when you stop, so its just an energy source. In the end, no matter what, you'll likely be fine. Just don't tear your arm off. In fact, its good to still move your arms in full motions so all the muscles can be stretched.