They can be stationary but flexy.

If you can build a cable for a 40Mm long space elevator, then bending said cable sufficiently to avoid space debris by a few kilometres should also be doable.

You'd end up with waves travelling up and down the cable as it oscillates due to natural resonance anyway, you could probably augment or dampen that resonance as needed to ensure the cable avoids the big stuff along its entire length. These waves would be basically unnoticeable to cars riding the cable due to the sheer scale of things.