Does procrastination imply knowledge of what is being delayed? When someone says he is procrastinating, does that imply that he knows which exact action is better than the action that he is currently doing? 

Is it called procrastination when you know that your current course of action is not optimal, but you don't know exactly what course of action would be better than your current course of action?
No. A person may claim to be procrastinating without putting any real thought into specific alternatives that are known to be better. For example, one might also claim this because one is aware of more socially desirable alternatives, which aren't necessarily better, or because one has been told by someone else (who isn't necessarily right) that one's behavior is procrastinatory.

A more general definition of procrastination may be found in the intro section of the Wikipedia article on procrastination, or on the procrastination tag wiki. I don't think the case you describe fits either definition, because not knowing a better approach implies that one's choice of approach (delay, presumably) isn't necessarily needless, but one may still choose this approach for purely rational reasons that have nothing to do with anxiety.