My bottle doesn't say anything about shaking. It also says the oil is emulsified, which I believe means it wouldn't separate. I haven't notice any difference between top and bottom.
BTW, I usually take mine by stirring it into my bowl of bone broth. There's no fishy taste, just a rich "base flavor" added.
I would shake it just to make sure the (lemon) flavor is mixed evenly. I didn't shake it and when it got down to the last couple of teaspoons, it tasted nasty...like fish!!! Hahahaha. =P Lesson learned!