Stick with your .22 RF for a couple of reasons. As you said, anything but a head shot will equate to meat loss from a .243 bullet and there's not much there to start with, but add on the fact that most shots are UP and that .243 is going to send those bullets even further into "who know's where it lands" places. At least a round from 22rf fire will use up most of it's energy when it hits a squirrel, even though the bullet will most likely always pass through, but a .243 bullet is going to go through the squirrel and have lots of energy left to keep right on going to who knows where.
Keep the .243 for shots at targets on the ground.