9V (6F22) Lithium battery recharging
Yes, you can charge Li-Ion "9V" batteries by a CC/CV power from a bench supply (8.4V and 150-200mA). I have a battery like this and have charged it using this method several times.

As you note the problem would be unbalanced cells. There's nothing much you can do about it, you can only count on the cells being closely matched during manufacture, but of course it's suboptimal.