A glass case is actually your friend, if only for limiting how much dust can collect.
Until you get the case, I heartily second Tanker's suggestion of a "blusher" brush. Cheap at the drugstore or supermarket. Nice and fluffy, too, so no danger of knocking things loos (if used carefully). A teeny, tiny, miniscule quantity of Electronic component dust spray (think spray with one hand, and barely touch brush to spray for this; or spray on a paper plate and use a drybrush technique) can be your friend.
Too late now, but running all your lines trhoug a beeswax cake before installing them will help prevent future fraying. Sometimes you can use a lit incense stick to gently (very gently, extremely gently, supremely gently) to "tease" the frays.
Use extreme caution, it's extremely easy to burn a gap in the rigging. So, heat/flame/ember is a last, last, last resort.
A case is significantly simpler.