After 30 squirrel kills with compressed air...
I would not consider any kit complete without a good high powered air rifle, and agree that cheaper and better are available than the Sheridan in the O.P. HOWEVER - personal choice in defense and hunting tools is highly individual.
As for lethality, I have lost squirrels poorly hit with .22lr I am sad to say. Have also lost some to poor hits with adult air rilfes ( Mostly a GAMO black cat ).
I have put down at least 30 squirrels some at very close range ( That will happen when they actually move into your home ) and one possum that thought it wise to take up residence in our shack.
The appeal to me with the air rifle is that the noise is less than a .22 and the ammo is generally cheaper and easier to carry. I also like beanshooters ( slingshots ) and archery tackle, especially home made.
Now living in Delaware, am looking forward to retiring to a state where I can roam with a nice scoped air rifle with a .45 Colt revolver or .44 Army black powder replica for just in case.
I really like the high powered air guns, you do need a REAL precise hit to take a squirrel out. Rabbits are a bit easier to kill it seems, have been told they won't do the job on a beaver's skull but will take groundhogs and raccoon at reasonable ranges ( less than 30 yards ) and precise brainpan hits.
I read about BP revolver enthusiasts talking about reduced loads in a .44 army for "popping rabbits" in the garden, the air rifle is a primo weapon for that.
They are accurate enough for head shots on sitting doves, of course you need a bunch for a meal but still, they will put meat in the pot. Would be fine for grouse, sitting quail, work great on bullfrogs, and have even taken the odd snake or three.
Bottom line, I love the high powered air rifle for being able to put down small critters without alerting the whole world to the fact that somebody just secured a meal. I say go for it and get the rifle you like. If somebody else wants to pay for it I would consider going with their recommendation.