Been thinking about this quite a bit. I think every lunar airlock will end up with a wash station and will end up using basic water sprays to get the job done. Soil compactors can be used outside to compact the dust and prevent it from being an issue during moon walks as well. I think once a moon base is established most moon walks will be on-base where dust would have been dealt with in the first few years and then after that it's basically like walking on compacted soil so it won't be loose.

And if you're wondering why they might use water for this well... water will be abundant and basically every habitat will have a municipal water hookup. A moon base might quickly find itself with several hectares of water and no where to put it. Might even end up injecting it into the ground where the water will be able to maintain it's liquid state (moon crust quickly reaches room temperature only a few dozens of meters underground).