Is there a way to kill the pigeons (or rats) without attracting the cops?

I'm currently going around and "collecting" all the pigeons, or flying rats as the game calls them (they don't look like rats), and it seems that 1 in 2 times when I shoot one I get a 1-star wanted rating and the cops start chasing me, which is a bit annoying.

Is there any way to kill them without actually shooting them and taking the chance of having to run around trying to get rid of the cops?

All pigeons must be shot unfortunately. And accurately too. For instance, I don't believe it's possible to kill a pigeon with a rocket launcher.

You could attempt to stand on a high-rise building and use the sniper rifle but I think that the cops are still able to detect this too. In fact, there are a few pigeons that can only be killed via sniper (e.g. around the airport) because they are so well-hidden that can only be viewed from a certain point far away.

There's no way to avoid the wanted level, you have to just put up with it.

You CAN in fact shoot a pigeon with a rocket launcher, has been the only way I've been able to get some of them.

You can also get them with a hand grenade if it detonates close enough to it.