Agree with the above. If dust is your primary concern, then your solution is as simple as getting different pads. A caliper cover is just trying to band-aid the real cause of the issue - the pads.

All pads create some level of dust. The material on the pad gets removed with use, so that dust is naturally released onto the components nearby. What the manufacturer can control is how dark the dust is (depending what material is used) and how 'sticky' that dust is (how prone it is to attaching to a surface like your wheels vs floating away).

I don't personally have any good recommendations for a low dust pad, but you should be able to Google search for pads advertised to reduce dust.

Keep in mind that in the broad spectrum of available pads, the highest performance ones will typically create a lot of dust as the focus is shifted to maximum friction and high temp stability instead of the amount of dust or noise as you would be concerned with on a daily driver. That's not to say you can't find a pad with acceptable friction for daily driving that is also low dust, I'm just suggesting you avoid getting a racy pad since that isn't what you are most focused on.

Also, some friction materials are more corrosive to wheel finishes than others. I bought Carbotech brakes for my vette and they're advertised as not being corrosive to wheel finishes. So even though they create a lot of dust, you could leave the dust sit for a long time and it all still washes off with no issues. Just something to consider since it sounds like your current wheels were damaged by this.