Vanessa wrote:
How do we adjust a too-large stainless steel watch band? (It's not
obvious.)

They are all designed a little differently but generally bands with
arrows are friction fit and the pin comes out in the direction the
arrow points. There is also (generally) a place on the underside of the
band that allows access to push the pin out. Every once in a while I
run into one that the only way to remove pins is to push them through
from the opposite side. Be careful you dont use a tapered punch that
widens out the hole when you punch the pin out. You may also need a
hammer to punch it out. They usually do any plating on the band with
the pins in, which works like glue alot of times. Take the same number
of pins out of each side if possible. If not, take the extra pin from
the 6 oclock side. If you find the pin wont stay in after relacing it,
use a toothpick to put just a touch of super glue on the end of the
pin. There is also (usually) some minor adjustment in the spring bars
in the clasp. Dont overuse that or the watch will clasp oddly.

I bought, at CostCo, the Wenger Swiss Military 200m water proof watch
for my teen-age son's birthday for about 30 dollars (as he wants to
learn how to scuba dive in Monterey Bay).
His thin wrist in no way fits this Wenger watch band, even wearing his
wetsuit, in so much as at least two links need to be removed from the
stainless steel watch band, one on each side. Instructions supplied
with the blister pack do not explain how to adjust the band (presumably
it's so simple that we should be able to figure it out by ourselves
using a butter knife)???

Presumably you will get it done at the jewelry store where you
bought it. Thats one of the drawbacks of buying this type item (kind of
like dive gear) at a discount outlet or online. They dont need
instructions.

His new Wenger Swiss Military watch band has six links on each side,
with two (I'll guess they're called) pins holding them together. The
three lower links on each side each have a 2 mm arrow embossed into the
center of the backside of the plates (for whatever reason, I don't
know). My son suspects that arrow is telling us the direction in which
to remove the pins holding the links to the watch band.

Hes probably right.

Further evidence these six links are the remove-me links are the fact
that a pin of some sort can be seen on a side view of the Wenger watch
band for these "arrowed" links only.

Problem is - how do we remove those 'pins'? If we punch them out with
an incredibly small punch (the pins seem to be about a half millimeter
in diameter), won't we ruin them? I mean, what holds them in? Friction?
If it's friction, won't we need new pins when we punch out the old ones
(presumably stripping the heads)?

They are probably friction pins and, no, you wont need new pins
unless you take them out regularly.

The other thing is these arrows are not symetrical in that they are
only lined up with one of the two pins per link (that is, there is only
one arrow per link and that arrow is under only one of the pins per the
link).
Am I missing something fundamental here?
What's the trick to removing and replacing two links in a steel watch
band?

Take it to someone that knows what they are doing and has the
proper tools.