I'm confused here as well;
How are you moving the rest of your stuff?
1) If by paid movers, let them figure it out, that's why they quote and they figure it out
2) If yourself (in a Uhaul), then you'll probably need to unload everything into smaller boxes, just like if you were moving anything else in your house and you'll put in the muscle to put it on the truck
If you ship it LTL, be aware it could go through many multiple terminals. I suggest you build a coffin (6 sided wooden box) to protect your tool box because it may very well get damaged. Don't forget it needs to have fork pockets.