Forget about oiling the teak if you're headed to the tropics. It is extremely hot underfoot, attracts dirt, and won't help the teak. Note that the three responses above are all from folks in northern climes, not the tropics. My boat was in the BVI for eleven years, and I've watched the trials of teak-decked boats there for over 30 years. Not pleasant :-(
The only real solution for aging/splitting teak in the tropics is to remove it. I had my teak tecks removed some 8 years ago, and couldn't be happier. I did put new teak in the cockpit -- by a master shipwright, using
epoxy and no fasteners -- and leave it bare. It still looks like new when I scrub it periodically.
Sounds like you don't want to do any major work on the decks, so about the best you can do is sand them a bit, try to patch the worst parts, and live with it. IMHO.
Bill