Cleaning - Sure, why not, as long as you do not damage the labels. I would probably use a damp cloth or paper towel and spot clean
Shipping - Yes, bigger items can be hard to ship. My rule of thumb (based on discussions with people I know who work at UPS and FedEx) - if you do not feel comfortable dropping the package from a height of 2-3 feet, then do not ship it!!
Markings - numbers and symbols on the base may yield some info on age, etc. Maybe...
Value - It might be scarce but I am not convinced that translates into a high value here. Two similar examples have been listed on ebay and have not sold, at least yet.
Old Crow dispenser #1 on ebay
Old Crow dispenser #2 on ebay