I use a .177 Gamo with field point pellets at ~1000 fps and it does work on squirrels out to 20-30 yards.
Since I am in a rural area, I often also use a smoothbore .22 (garden gun) with .22 shotshells. It’s louder than a pellet gun, but #12 shot will not travel more than 150 feet even if the gun is fired at a 30-40 degree angle.
The whisper looks like a good solution.
Do you have to sight in the scope or does it come as a package more-or-less sighted in?
Will that Gamo dispatch rabbits? I have that problem, but live in the city limits, so they don’t look kindly upon things that go “bang.”