Add-on Aero Bars to an Already Aero Handlebar
Most clip-on aero bars attach near the stem, where the handle bars have a round profile, not where the bars have a flat profile. The elbow pads are outboard of the mounting point, which will put them over the flat portion of the bars.

As an aside I would try to assess why you are experiencing wrist issues.  You may simply need adjust your setup. It is also possible that on the new bars you are twisting wrists. Ideally you want to keep your wrists straight as possible. You may need to adjust the position of shifter/brake on the bars to help facilitate.