In practice, parts of shakers rarely fit well. So these are a pain to handle. Strainer tops are very loose in many models. So they can leak when using shakers. However, wetness shouldn’t cause leaking. Wetnesses causes a tight seal. It makes it very difficult to top off when everything has contracted because of the cold.
Further leakage is also possible – the shaker may leak from the previous drink because it is cold. Shaking should form a seal the tin to shrink. If you put it already cool then no further shrinking. So irregularities in the shape between the various parts can cause a leak.