Obviously there's the conservation of momentum to deal with. That fleck of paint has a decent amount of momentum but that's fairly easily absorbed by a couple of tons of material fixed to an otherwise rigid body.
You'd probably attach it via cables and if, somehow, enough momentum was delivered to that "paddle" that it would tear off the cables would just let it go.
If the paddle is fixed to the ring and is let go, it's just going to fall to Earth even with any added momentum, in which case it'll burn up in the atmosphere.
The more dangerous debris is larger stuff. Like there are dead parts of rockets, even smaller stuff like bolts. These pose extra challenges but a lot of the same principles apply.
[1]: https://www.csmonitor.com/Science/2016/0513/Space-debris-dan....
https://en.m.wikipedia.org/wiki/Kepler's_laws_of_planetary_m...
You can only collide with an orbiting object if one of you is changing orbits.
It's very difficult to force to objects to meet in orbit with nearly the same velocity; it requires complex active maneuvering.