I am an American; if I were going to live in Japan for any amount of time and conduct business, on official documents, could/would I write my name as Americans do (first-last) or as Japanese do (last-first)?
In most of the time you're going to keep given name first, unless otherwise designated (like in some application forms). Japanese know, and expect that Western names (actually, almost everywhere outside East Asia) are expressed in this order.
However, you may see your name spelled with family name first in some documents, when they are compiled for indexing purposes (e.g. employee list). It doesn't mean you'd be addressed in that way, though. If you're asked to tell your name always from the family name, I'm sure that it's a very special practice in that industry.