I am looking for a book whose author or title, I think, begins with
the letter "I".  It is about a man who is an assassin and enjoys cave
exploration.  He has learned how to sense when people are near him or
when he is close to an object.  The book tells that he is able to kill
with ordinary objects like a drinking straw or a plain piece of paper,
but does not go into any detail about how to perform such things.  He
also is into Japanese culture, ie. arranging rocks in a stream to make
the most melodic sound.

Hello.

I believe that you're thinking of "Shibumi" by Trevanian.

From a reader review on Amazon.com 

"Nicholai Hel is a hired assassin who has certain esoteric knowledge
that he uses to excel in his craft. Shibumi, which is a special state
of clarity (meditation) was something that just came naturally to him
since he was very young. The proximity sense, which can be used to not
only sense the presence of others, but also to read their mental state
was developed when he was serving time in solitary confinement. It was
also mentioned that he became skilled in the art of Naked/Kill which
enabled him to kill with virtually anything (i.e. a sheet of paper, an
ID card, plastic straw, etc.)."
http://www.amazon.com/exec/obidos/tg/detail/-/0345311809/

The part about cave exploration (spelunking) is mentioned by another
reviewer on the same page:  "Spelunking bits read like..."

---------
search strategy:
spelunking assassin

I hope this helps.

Your response was quick and informative. Thanks.