Don’t try anything too complicated here, a feather duster is best for the job, and should only need to be done, in an average household, once or twice a month. Any cleaning solutions could react badly with the liquid art and cause the Swarovski crystals to come loose.
If you have to move your Art for any reason always carry it by the string on the back of the frame. It is a heavy product and lifting from top or the sides puts a lot of pressure on the structure of the frame and could cause the joints to pull apart forming small gaps.
If transporting we would recommend lots of bubble wrap. DO NOT directly blanket wrap, the fluff can can stick to the liquid art and catch on the crystals.