Having them dangle on string could be tricky, they'll move in any breeze, OTOH they may also be deflected in the same direction as the breeze and pellet making it easier.

A simple wire tether could stop them doing their disappearing trick.

Even simpler, a couple of feet of coloured string tied around each would make locating them easier, rather like those "tag things" for errant skis, whilst still allowing them to fly.

The benefit of the paper targets is you can see where you miss, as well as easily show the rest of us how it's going, and those without empties can have a play too.

Looks like there's only you and me doing this at the moment...