I know that Clavell based his protagonist (loosely) on the adventures of William Adams; a 16th century pilot of a Dutch ship who rose to become Shogun Tokugawa Ieyasu's favorite "pet" foreigner, bequeathing titles, lands, and honors on him (while also forbidding him to ever leave Japan).

I also recently learned that by the 16th century, bathing had fallen out of favor due to many factors, including the popularization of the "miasma" theory of illness vectoring. Here's Lucy Worsley explaining it in her "History of the Home: bathrooms" series:

https://www.youtube.com/watch?feature=player_detailpage&v=inoVg5a1kps#t=510

So, it is entirely possible that immersion into the water was considered a cause for concern for a 16th century Englishman. But to think that the English in the 16th century were not aware of bodily odors would be a misconception; they washed hands, feet, and face, but preferred to wear linen underclothes which would wick away the dirty body odors and grime while perfuming themselves to disguise the smell of their bodies.

This is complicated, though, by the fact that he would have been on a ship for about a year by the time he was shipwrecked off the coast of Japan. The main way to launder clothing on a ship was to soak it in urine (lye-based soaps wouldn't clean anything since they don't lather in salt water and the ammonia in urine was very effective at removing stains like blood and tar), so even if he was 'clean' in the 16th century English style, he would still stink.

As for familiarity with water, remember that there are a few complicating factors; a) while sailors know their way around water and deal with bilge and waste water all the time, they don't bathe in it - that's just weird to them. b) the sea was a harsh mistress and to fall into it was to drown or be eaten. I've read - though never confirmed for myself through primary sources - that it was even considered "bad luck" to know how to swim since you were tempting fate. C) falling into water, being rained upon, or whatever is wholly different from voluntarily immersing oneself in water on purpose; to the 16th century European mindset it was akin to doing the breaststroke in a sewage treatment plant; just asking for trouble.

So yes, while he may have tried to stay as clean as he could, he stunk. And he probably knew he stunk. But he was still probably terrified of immersion bathing.