I own and shoot both break barrel springers and pcp. Knowing what I've learned over the past few years and what I've spent along the way achieving that knowledge, the pcp guns will spoil you with their consistent accuracy and lack of recoil.... recoil which lends to the downfall of springer accuracy, especially out to 40yds. So yes, the obvious gun would be a quality barreled pcp…..but now you need to fill it every 30-50 shots, it is a more expensive (tank-compressor) or tiring (pumping) endeavor.
IF I were to do it over again, knowing what I know now, I likely would've spent more $ on a higher quality spring gun with a higher quality trigger and spent more time learning the ammo it shot best and the best way to rest it for consistent hits at 40yds.
I'm guessing your squirrel problems are REDs, they're the only species I've had issue with chewing their way through to gain access, and they are always a challenge to shoot, unless they're sitting still and eating. Good luck with your rifle choice and elimination of the pests.