The first question is do you have your own boxes? This might be a larger savings than you think when it comes to shipping. Specifically, you need to find out the most common dimensions you are going to ship. If you go to the UPS store or some place similar they will charge you $10+ for the box alone. If you get custom boxes, not only will they be cheaper but they will probably keep your items safer from the perils of shipping destruction.
Second, if you are shipping things that are the entire sheet of proof grade you are looking at like $20-$25, or more, for just the dimensions. This price was based on using UPS’s flat rate shipping prices. I am sure you have probably figured this one out. So the first thing to get the price down is to produce smaller products. IE, don’t ship things that are the size of a full sheet of proofgrade unless you are will to charge a ton for shipping.
I know a lot of people who sell like the laser cut letters on Etsy stop at the 12x12 inch size and use the baltic birch plywood that is on Amazon. This is the reason the cap their letters sizes at 12 inches. It has more to do with the size of the material they are using.
You can look at the flat rate boxes from the USPS but they aren’t that much cheaper and I am not sure you would get the insurance coverage of shipping with UPS or Fedex.
Personally, I ship a few products that are entire sheets of proof grade material. I end up having to charge $50 for them because half the price is eaten up by shipping.
Most of the other items are much smaller and the shipping isn’t that bad on them. So if shipping is a problem, maybe specialize in smaller items.