In ASL, if you shake W's towards each other, you get "war".
( a push-pull sort of conflict sign, with W's for war. )
Accurate as the connotations might be, you might avoid that
for the official sign.
I suggest don't try to make cute puns a language unless you are FLUENT
in it -- or you may get more than you asked for. Depending on exactly
how the internet sign was done, I could see more similarities to "pain"
than to "friend". I think I would have modified it to be more like
"story" with "wire" handshapes. Would have retained the initial "i"
handshape, which is nice.
I'm hearing, and I'm not fluent in signs, but I'll suggest the following anyway.
If you want a sign for WWW, a very easy one is also very natural, and
that is simply to sign W W W. When a single letter, (particularly one
with a handshape like W) is repeated, you don't open and close your
hand three times to make the W's -- rather you lean the W forward and
down, fingers straight out almost horizontal, and kind of bounce
downward thrice, each time a little to the (right-handed) signer's
right from where the previous one bounced. The third time down, you
hold it there a moment, and don't bounce it back up. This
leaning-forward and boucing-to-the-signer's-right is readily understood
to mean repitition.
It would be like the sign for the number "22" or "33", except thrice,
and in ASL the number 3 uses the thumb, index, and middle fingers,
whereas the W uses the three middle fingers.
It has the advantage that a deaf person who does not know your
secret code sign for WWW would still see "WWW", just as if you said
"WWW" to a hearing person who did not know what WWW means, but could
recognize it later, or plug it into context hearing "World Wide Web".
("World" uses "W" handshapes, and "Wide" can. I don't know web. )
The only danger I can see with "WWW" is some similarity to "world war
2" or "world war 3". The context of this proper noun is different
enough from that proper noun that it's probably not a problem.
The best signs come not down from above, bestowed graciously on the
deaf by a hearing authority, but rather trickle up from below, from the
actual communities and their living languages... and there should
be some deaf communities somewhere on the net, but I'm ignorant where.