No, Kid vs Saint Shanks has no build-up besides that "I lost my hand against Saint Shanks" moment from Kid, which explains why they planned on going after him previously. Saint Shanks vs. BB goes deeper than most of the biggest rivalries in the series, which generally lack the kind of animosity that Saint Shanks and BB have b/w them. Saint Shanks even went out of his way to ask WB to not get involved with BB. Kid has strong ties with Saint Shanks too, but BB's legit Saint Shanks's nemesis. Among the people who have a chance at killing Saint Shanks, BB's the foremost.