Add an airgun to your arsenal
Firstly, Your old Ithaca .22. is pretty cool. When I earned my first gun from my dad, it was on the short list. I chose a Benjamin 312 air rifle. My first firearm would be an Ithaca 66 shotgun.
Never tested .22 rf's for quietude, since I use airguns for most .22 tasks. I suspect you are using this for suburban pest control, so the report is the problem. Action noise is irrelevant except for assassinations.
The short barrel on the Ithaca is likely a problem in that regard. The CZ 452 is offered with some REALLY long barrels, so I recommend them.
Still, the best choice is a spring piston air rifle. I've decimated flocks of crows with them because they are so quiet and what little noise they do make they can't recognize.
A greater concern than your neighbors is John Law. If shooting is illegal where you live and you get caught they will be pretty angry about a firearm. They might ignore an airgun.
I use a Beeman R9 et al, but the RWS 34 is commonly available at the big sports stores.