I would think you could use the same arrows. You may need to increase the point weight 50 grains or so to keep the arrows flying right. Doing this will affect your speed, but it will increase the stability of the arrow and the penetrating power of your setup as well.
If you do get a new bow, I wouldn’t change anything right off. Just start shooting the new bow with the old arrows. Different bows like different arrows. So you may not have to do anything at all.
Reducing the bow weight reduces the energy you put into the shot. Therefore your arrow speed will, necessarily, decrease. Unless, of course, your new 45lb bow is of a much better design than your 50lb bow.
How’s that for wishy-washy?