Airsoft guns are not "air weapons" under the Section 57A.
This changes when we breach the "lethal" power limits as described.
If this is a bolt action gun then this becomes an air rifle by legal definition, which unless you're in Scotland, won't get you in any hot water for ownership, but a site would be screwed if somebody complained of an injury and it was discovered you were over the limits and had technically injured them with an air rifle.
The same can be said for fully automatic airsoft guns, although once these surpass the specified limit, they become Section 5 firearms, meaning there's no legal variation between your airsoft gun, and a completely bog standard real M240B.
As already stated, the UK firearms law is incredibly poorly written, with far too many overlaps and grey areas.