A thicker wash which can then be scrubbed off with a piece of cloth or sponge may prevent you going overkill with the grime. The ones Warlord Game sell usually work for that, otherwise leave a Games Workshop wash without its lid for a while and it'll give the proper consistency.
Personally I add a bit of paint to my washes to thicken them up and allow for a wider range of colours. I paint tanks and buildings mostly, but it should apply to airships too.
Usually I'll do a dry brush of a light brown first for dirt. Then apply small dots and spackled brown/ grey / black for more dirt as required (probably overkill in scales smaller than 20mm). A yellow wash / light brown mix does for built up dust in cracks.
For rust its something similar. Various orange wash / orange / brown paint mixes. I tend to add paint to the wash as it dries on the model too to give more colour variation.
Plus the whole model will have received a dark brown wash and highlight prior to this, so overall the thing will look a bit dour to begin with. However, this all may be overkill for VSF style airship as you may be going for a cleaner appearance, as opposed to a diesel punk look (I'm due to make some VSF steamships, but definitely will be going for the dingier end with my own models
) .
Edit: And I suppose a consideration would be that if the vehicle is in the air, it should be weathered differently than something on the land or sea. Depending on how often its moored (and liable to receive dirt from the ground), it may be cleaner than a regular ship. However similarly you may want to add more rain streaks and liquid related weathering as it may spend times in clouds - leaving off so much of the dust effects.
Grey would work for rain and dirt streaks. Black would be more overtly oil streaks, which you may want to apply to metal components. I'd give the material a darker tone so that the streaks don't stand out so much, or even go ahead and go pretty dark, and have the streaks in a lighter tone - washing away the dirt.