What is the ruling regarding someone who swore inadvertently not to wear a specific pair of shoes, and then wore them?

Since you swore inadvertently, and the oath slipped from your tongue unintentionally, this is a "laghw" (vain or idle) oath, and there is no expiation for it. This is based on the Almighty's saying: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended of oaths." Therefore, there is nothing upon you for wearing the shoes you swore not to wear.