It's quite a nightmare, particularly when you are trying to figure out if this stuff can kill people you want to send into space. The only real mitigation is lead-based solder and coatings on components.
Cleaning? That can be both dangerous and highly ineffective. The whiskers are very strong due to their molecular scale. Mechanical brushing might fracture longer whiskers. Then you have the problem of ensuring that they don't go under devices or in-between contacts. The process would likely have to be repeated many times and include both manual and automated optical inspection as well as x-ray imaging (which might not be able to detect fine whiskers). And then there's the reality that you probably don't want to inhale these things at all.
So, off to the landfill we go. It is likely better to build a new board than to try to clean one. I can't even begin to compute the delta in carbon footprint between making a board with lead-based solder that will last decades and the "clean/green" RoHS board that is sure to end-up in a landfill (cleaning/fixing it is bound to have a massively larger carbon footprint that making a new board).