Build your own delegation, if you had this:
$("#wrap").on('click', '#myID', function() { console.log("clicked!"); });
All it really does is:
$("#wrap").on('click', function(e) {
if ( e.target.id == 'myID' )
console.log("clicked!");
});
So for your custom events you could do:
$("#wrap").on("tapone", function(e) {
if ( e.target.tagName.toLowerCase() == 'div' )
console.log("tapped!");
});