Let us assume for the sake of discussion that the biblical account is
true.
As I read the bible, circumcision was meant to be a sign of a covenant
between god and the Israelites solely for their own purposes -- not a
sign of their covenant for the information of pagan peoples. After
all, most of the pagan peoples in the middle east at the time were also
circumcised, so freedom from foreskins was nothing special. As to why
the foreskin was chosen for sacrifice -- rather than, say, the ear lobe
or middle toe -- the reason must be that it is the most useless and
readily jettisoned part of the body. It would not be sinful for
witnesses to observe the infant penis during circumcision itself -- in
fact, witnesses would be necessary to prove to the community that the
covenant had been observed. The male would thereafter be considered
circumcised by repute, not by repeated public displays of his penis.
God, with his infinite wisdom and all-seeing eye, would know all about
it too.