The only wide exception to this tends to be country names which mostly seem to get a global and a local name. There's no real reason to do this when using toki-pona.
you could go for constructs like "ma pi suno tewi sewi" which'd translate to "land of the rising sun" or more literally "land of the sun going up" but I fail to see the point. Any toki pona ''native'' would be able to read and pronounce "japan" since all the letters are available in the toki pona alphabet, the pronunciation even matches well enough. If someone doesn't know japan they won't know what "land of the rising sun" refers to and you'd need to reach for more descriptive language in any case.
Disclaimer: my grasp of toki pona grammar is tenuous at best, I'm sure there's better translations for "land of the rising sun".
As for how my device supports words not on the list because as you smartly noted it’s optimised to the vocabulary size so how do you add randomo loan words? Thankfully the hieroglyphic display orthography I’m using has the same problem. The solution is to do it nato-alphabet style, and put the loaned word in a cartouche. Which is very labour-intensive to read as well as to write.