A is simple past, not simple present. Your analysis is correct.
B is present perfect, as you said, the action of not having shaved is still in progress, but what time of the day is it? In A, what time of day is it?
Both are past tenses:
A - Simple Present. The action is finished. You definitely didn't do that in the morning.
B - Present Perfect. The action is still in progress. You have not done it yet, but you decide if you do it later.