Some plums take alternate years off, so you should get plums next year.
Pruning in wet weather - definitely not, because you run the risk of introducing fungal disease.
Pruning generally - plums are not pruned regularly in the way that, say, apples are. pruning just encourages more growth, so should be restricted to removing damaged or weak branches. They are big trees, and pruning won't change that, but make it worse.