Doing the arms in a similar but not quite the same color would probably look weird. My suggestion would be to start the sleeves with the old ball and do the bottom of both the body and the sleeves with the new one. In between, knit rows alternately with both balls for at least 10 cm to make the colors blend together and get a smooth transition. That way, depending on how different the dye lots really are, it will either be barely noticeable or at least look intentional.
It’s pretty common when working with hand-dyed yarn since, well, those don’t have dye lots.