If you have a shoulder injury why don't you hunt squirrels with the 22
You will find they are much more fun to shoot and easier to clean also.
I bought my 12 year old son a S&W M&P 22-15. I love the little thing so much I may go get another one for myself.
Shoot them when I get the chance. Have a dozen or two .... majority in 5.56 caliber but have other calibers in the AR too, like 5.7x28, 7.62x39, 6.8spc, and 450 bushmaster. All a hoot to shoot. I build precision and regular uppers. Sell some parts and uppers on gunbroker.
Note on twist rate for 5.56 - get a 1x7 or 1x8 for it - will stabilize the heavier bullets like the 75 and 77 gr.
Today's "normal" 1x9 typically won't stabilize the heavier bullets. YMMV
Shoot straight!