You can fit 120 keycaps into a small flat rate priority box. That will cost you $18. Using the small flat rate box also allows you to use the small CN-22 international customs form, which provides delivery tracking within the US. You cannot add insurance to this option.
Once it's airborne, your tracking number no longer works within the states. But in some cases, the same number is passed onto local/domestic posts and is trackable via their domestic website. This is rare, but definitely a bonus if it works.
Edit: Pros of using Priority = Faster. Pros of using lysol's method = cheaper, safer, and ability to insure. Given what you've said, I think lysol's method of first class + registered mail is the way to go. Make sure you get a box though, don't want any crushed keycaps.