I leave layer cakes alone and bought 12*12 plastic containers w/lids for storage. Charms are different. I keep them bundled until I start using them. I find that sometimes I find just the right pieces for a project in a charm pack. I have clear shoe boxes, again, w/lids stroring packs "broken" by color. Some charm packs I have stored with rubber band to keep them together.
In orther words, find a system that works for your "searching" method.