Perhaps a blow dryer set to its cool setting and lowest blow setting would remove some dust. For silk flowers, there are spray cans of cleaner available. For stubborn dust, a soft paint brush may work. Be sure to use a soft touch when using the paint brush.
I used an air compressor, but held the wand a few feet away from a wreath. I wouldn't do this with fragile dried flowers, but for silk or eucalyptus or some other sturdy flower, it works great. Just be sure to stand upwind because the dust will fly!
It depends on the dried flowers but I have used the kitchen sink sprayer on eucalyptus and baby breath swags with good results.
i once laid a silk flower vine on the driveway and sprayed it with the hose. i left it outside to dry in the sun. worked better than i expected.
I use the canned air they make to clean computer keyboards etc., available at any office supply. Just remember to use short burst of air rather than a long stream. You will have to experiment to find a safe but effective distance to spray in order to clean with no damage.
I use a gallon size plastic zipper lock bag and add a good amount of table salt to it. Place flowers in the bag and zip closed. Move the salt back and forth through the flowers. It will move dust and dirt very well. The sturdier the flowers (plastic/fabric) the harder you can shake the salt. I put the stems in the corner and hang on to them and shake away. Best of Luck! P.S. In the case of wreaths and garlands, you could put them in 13 gl. bags and use the same technique perhaps.
I use Silk Plant Cleaner that I buy at Walmart. I tried it on several different type of flowers that are fake and dried. Take your flowers or plants outside and spay on the cleaner Let it set outside until dry. I usually do a pretty heavy spay on any that are plastic or silk. I've never had to respray the whole plant or flower as it cleans them the first time I do have to spay some of the parts that I missed because they really stand out. With dried flowers I spray them very lightly, sometimes I do this a couple of times. Always let them dry completely between spays or they will wilt.