In some places, any air rifle that has over 12 fpe is considered a firearm. Because of that, their entire airgun industry is based in -12 fpe airguns. If you watch some of the videos, you will see they don't look like they need any more.
I grew up killing squirrels with a Crosman 2100. It never made 12 fpe in its life. Squirrels are tough. You hit a rabbit and chances are it doesn't go anywhere. A Squirrel will take a fatal shot, jump to another limb and then climb ten feet to a hole. Figure it this way.
If you give their chest 2 inches wide, and then put a .22 through it, for me that would be a 1.7 inch wide or so pellet through my chest. There is not much chance of me going anywhere far. A squirrel will try at least, unless you shut him off on impact.
The .177 did fine at that, if and on;y if you hit them like you were deer hunting. I mean you have to pick the spot and then hit it. You cannot simply aim at the squirrel, anymore than you can simple aim at the whole deer. My uncle thought the head was the best eating on a squirrel, so i mostly shot them in the body with the rifle.
Because of the close range, i also tended to use target pellets to increase the initial impact effects.
I got a .20 and at the same ranges, using wadcutter pellets, it would knock squirrels sideways off the limb with a solid hit. Then I got a .22.
.177 is fine, if you put that pellet where it belongs. If you don't, then they get away hurt, with all that entails. A .20 will make a noticeable improvement in anchoring them right there. A 14 grain .22 will anchor even more right there.
An old saying, and I am not saying it is correct, but it has the correct spirit from what I have seen/experienced. In low powered air rifles like i grew up with, the saying was, .177 for feathers, and .22 for fur. The feathers on a bird can gather around a pellet at those energy levels, like a shotgun pellet hitting a turkey, and the .177 penetration was desired. The .22 was recommended for fur, simply because it works better when you miss by half an inch on something like a squirrel.
Just one opinion, and i readily admit to having killed a lot of squirrels with a .177 in this energy level or below.