I have a lot of experience jumpseating around the world on cargo and passenger carriers. Here's my advice:
You can take a cargo airline (Kalitta/Atlas/Western Global/UPS/FedEx) to Narita, Japan (NRT) and connect to one of the 3 daily non-stop United flights to GUA.
If you don't want to deal with the hassle of customs, I would get to HNL first on UPS or Alaska, then take the United B777 flight that leaves at 14:15 to GUA.
The alternative would be to jumpseat for free to any large eastern Asian airport on a cargo carrier and buy a ticket to Guam from there. Kalitta, Atlas, and Western Global allow off-line jumpseaters to jumpseat international. UPS and FedEx do not... hopefully YET.
My arsenal of resources for jumpseating are Staff Traveller phone app (for loads), Passrider.com,
ALPA Jumpseat website (to find out how to list and obtain cargo schedules), and believe it or not, Wikipedia. Wikipedia has a section of "Airlines and Destinations" of every single airport that exists in the world that is constantly updated by the savvy crowd-sourced nerds of the internet. It'll tell you which passenger and cargo airline flies where non-stop from that airport.
Good luck!