If you just want to plink in your backyard then just get a BB gun that shoots steel BBs. And only use iron sights which will teach you instinctive aiming. I'd say that's actually way more fun than a scoped air rifle. If you're not going to be head shorting squirrels then you don't really need the accuracy of a dialed in air rifle. Looking in a scope at a piece of paper and shooting the same hole looses its appeal pretty quickly.

For Air rifles you can have a bullet catcher that is basically a funny shaped tin can you put your paper target in front of. It will collect the lead if you hit the target.

You can get pellets and ball ammo in other materials. Might have to special order them, not sure how available they are over there, but they do make them. I have steel ammo for my air pistol, it's my back yard pleasure shooting gun, so lead isn't acceptable to me.

I can't be asked to get a license for a proper firearm

My god, what tyranny you live under, please tell me what authoritarian country you live in so uncle sam can come free you after we're finished with Iran.