"I'm trying to add a little bit of muscle weight to my body (while of course losing fat). "
Bzzt. Stop reading.
It's basically a myth that you can do that. While it's not exactly technically "impossible", for all intents and purposes it mostly is. Your body requires a calorie deficit to lose fat, and requires a calorie surplus to build muscle. So you cannot do both at the same time.
If your morning shake needs to be low protein does that mean you're getting enough protein from food sources already? A shake is a quick and easy way to get some healthy food in in the mornings, but it doesn't have to be a white-powder purchasable processed product!
Get a blender and make your own smoothies. With skim milk or with water, you can add fruits, yoghurt, ice or vegies and get a healthy start to your day and good nutrition without the added chemicals.
There is no need for a "protein powder" if you are not deficient in protein. The "morning shake" idea is not so bad, but it doesn't have to be that product.
If you want to gain muscle and lose fat, switch back and forth. Lose some fat on a deficit first, then spend some time on a surplus to gain muscle.
Deb, in New Zealand