Most of our hotels in the US have laundry facilities...both RMS and HHN in Europe have machines also...
If you (sorry, as a 767 pilot, not likely but could happen) make it to HKG, ICN, PVG, etc cheap laundry shops near all of our hotels...SYD hotel at Coogee Beach, I don't remember.
I can't afford exofficio (!!) but I've been wearing Columbia, North Face, Eddie Bauer, etc quick dry stuff for a long time...and sorry, I don't do laundry in the sink!! I plan ahead and get it done at a shop (in Asia or Mid East) or use coin-operated machines.
Another thing to remember is to have a "cruise shirt" available on the freighters so at TOC (definitions vary!!), you can jump into one and get an extra day out of your white uniform shirt...