Among the OAK Collection watches up for auction are (left to right) a Patek Philippe split-seconds chronograph, a 1962 diver’s watch by Breguet. and a semi-skeletonized Akrivia wristwatch.

Sly might be late on set. Sylvester Stallone is auctioning off part of his staggering $7.5 million watch collection at Sotheby’s starting on June 5. The highlight of the lot is the “Rocky ...