How to accurately set up shipping costs based on box dimensions?

[D-Signs-Design]

Hello,

Ok, my site is pretty much ready to go live, but I really need to figure out shipping before I can. The problem I'm running into is as follows.

My company is basically print on demand for signs and business promotional products. I have my vendors that I am using to source the products (not a POD app) from which I will order after a order comes in on my store and I will blind ship from my vendor to my customer. I have products that have a lot of variant options. I am utilizing an app for the variants so for example my customer wants an aluminum sign, then they pick which size they want, the size they pick changes the price, and it will also need to change the shipping costs.

I started setting up the shipping by putting a weight for each variant option and then setting shipping values in Shopify like 0-1 lb is $10, 1-10 lbs is $20, etc. The problem I'm running into is that even though say a customer wants a 48" x 36" aluminum sign, that sign weighs say 8 lbs, so that would fall in the $20 shipping spot, but when I simulate how much the shipping is on my vendors site , because of how big the box would be at that size the shippings cost is like $160.  But if it were 8 lbs in a small box obviously the shipping would be a lot less expensive.

So, what is the best way to set up my shipping costs? Is there a way to price it by the dimensions of the box rather than the weight? I will not be packaging anything where I am at and will not be printing out any labels, etc. I will simply be receiving the order from my store, then going onto my vendors website, ordering and blind shipping it to my customer. I just need to find a way to match the shipping rates that my vendor is charging. 

Thanks so much,