First Springer Either a Diana 54 Air King or a Weihrauch HW 95L Field pro

Have you considered a .22 cal Walther Parrus? The muzzle is already threaded for an air stripper or sound moderator or whatever you want. Plus, they are very affordable, high quality German, you get the idea.

I have a Diana 56 and even with a good sound moderator, its loud and that's because the stock acts like a sound board on a violin to amplify the sound. I would imagine a 54 would do the same. It will be loud.

A lot of people will recommend a .22 cal Diana 34. However, as you have noted they have that plastic front sight assembly thing on the muzzle. The older ones do not. So, look for a used/old 34 and consider a DonnyFl muzzle adapter. The DonnyFl muzzle adapters are available for a range of barrel diameters.
 
I'm seeing many comments injecting biases, confusion and not addressing the OP's question. I do own a .22 D-54 and like it very much.

#1. The OP asked about a HW95 and D-54. These are two air rifles in different classes. The HW95 is a break barrel advertised at 755fps (18.1fpe with a 14.3g pellet) and the D-54 is advertised at 900fps (25.7fpe with a 14.3g pellet). Not in the same power league. 755 will kill a squirrel at moderate ranges while the D-54 will be able to stretch the range much further.

#2. I do not feel a subsonic springer needs a moderator. My D-54 is not loud and the noise it does make is mechanical noise, not muzzle blast, so a moderator wouldn't do anything for that.

#3. I'm guessing most posters are not 6'6", 220# and in good shape. I'm very close to this and carry my D-54 around. It is definitely heavy but with a sling I don't feel it's a problem. If you tried to hold it in an offhand shooting position for 5 minutes that would be a problem but most shot opportunities are only seconds long. Being in shape makes a big difference.

#4. Not sure where the $2k figure came from about getting into a PCP. A simple Discovery/hand pump combo for $400ish will be more than adequate for squirrels. A Hong Yeng compressor instead of the hand pump for $300ish is a good option. There are also other great budget PCP's that offer good accuracy and features for $200-400.

My 2 cents.

Doug
 
If your shots will be up to 30 yards , why not a HW30 Urban Pro ? It come with a quality Weihrauch scope and silencer. Steve at AEAC tests it out on YouTube. He was getting penetration using gelatin , and that .177 would go right through a squirrel . My FWB 124D has killed many rabbits and ground squirrels. The HW30 Urban Pro from AOA is about 6.5 pounds with scope and silencer. Need more power , then the HW50 teamed with a scope and silencer is available , and weights 8.1 pounds. I had a Diana 54 , and that is one heavy gun. So is the AA TX200 , which I had as well. The HW97 is 8.8 pounds bare , but AOA offers a silencer for $100 more.