I have some small parts that need to mail to Toyko. Looking for suggestions on cheapest way to go when time is not an issue. Thanks

Ugh, Ill relay my .02 as I am in the process of suffering a shipping related debacle right now.
Shipping can be a PITA. I found that historically USPS handled small things including international pretty well. While larger Items were better (more economically) handled by firms like Fedex.
Ive had no issues shipping to Japan.
BUT, Im not sure this a recent change to their effectiveness, or some other anomaly, USPS has gotten WAY worse!!
The most egregious example is a parcel I shipped to Germany....In August! STILL hasn't been delivered~
Ive expended many time the value of the parcel in time tracking & then begging on the part of my customer for USPS to either effect the delivery or return the PKG ...to no avail. So frustrated

My rule of thumb for International shipping is: Under 1 kilo = USPS. Over 1 kilo = UPS or DHL.

I have had really good luck with USPS (agree for large items other carriers do better.
There on-line if you have an account will allow you to compare services. & click boxes for any taxes or import duties. My local counter team are REALLY good and will look at all options.
Their "Flate Rate" (small, med & large) unless heavy for its size is more expensive than using your own box.

During the Pandemic overseas shipping has been a nightmare. Packages big and small have taken forever, but most have been delivered. But really, forever, like 5 months to get wheels to Australia. I think some of it is the shortage of staffing in the custom's offices. Tracking will show the item arrive in the country in a couple of weeks, and then not move out of custom's for months.
The rule of thumb is usually USPS for International. But it's slow right now. But so is everybody else. DHL lost two packages going to the UK, after they shipped them to the UK, then Germany, then the UK, then lost.

Patience is key right now.

ParcelMonkey.com
My experience has been excellent.