Like rainbowgardener said, cross pollination does not affect the fruit (in this case squash or zucchini). The fruit is entirely made from the ovary of the plant being pollinated and thus contains only the "maternal" genes. The seeds inside of the fruit do, however, have both maternal and paternal genes.
If you grow those seeds (F1 generation), you get a fairly predictable mix of traits (think of a mule) from the maternal and paternal plants. If these F1 plants then cross pollinate, the new seeds will be the F2 generation, which will be a much less predictable mix of traits (if they develop at all-- many F1's are sterile...like a mule), because recessive traits can come through (which is why it's not a good idea to mate with your relatives).
for more on the genetics.
Bottom line: cross pollination is not a factor unless you save your seeds.