Any airgun that is powerful enough to use for hunting will be classified as a firearm. Therefore, it makes sense to just get a .22 rimfire rifle instead.
The "over-the-counter" 495 FPS airguns that you can buy without a PAL mostly don't really reach that velocity. In my experience, they're tuned so that you MIGHT get near that velocity if you use some super-light alloy pellet. Using normal weight pellets you get more like 380 FPS.
My Crossman 2289 "Backpacker" was rated at 495 FPS. With Crosman 14.3gr pellets it would do about 350 FPS out of the box with 10 pumps. After modifying for more valve volume, weaker valve spring, heavier hammer spring, steel breech, 18" barrel, it'll do 490 FPS with 10 pumps, and 590 with 25 pumps (using 14.3gr pellets). At 590 it packs a wallop. 490, not bad. Out of the box at 350 was useless.
(Yes I have a PAL for my over 500 FPS pellet gun).