Technically, your best bet would be have the item set off a common event which turns a switch on, which in turn enables the parelel process of running.
However, common events cannot be activated be equipments. What you would have to do, is create an item version of the shoes, have it run the common event, then present the player a choice, of whom equips it, and use the common event to give the player the 'armour' version, delete the 'item' version, and then equip it on the person of choice, and activate the run switch.
Convoluted, I know, and also causes issues if the player removes them (since that doesn't trigger the event...a player could just wear them, then de-equip them and still run). But I can't think of any other methods that don't check each and every character (except scripting the check directly into your Scene_menu as it closes...but you'd have to ask at RGSS support for that kind of thing).