If you disable the built-in delete icon using eventDeleteHandling="Disabled" you will be able to add a custom icon using active areas. See also an example in the docs (https://doc.daypilot.org/scheduler/event-deleting/):
<div id="dp"></div>
<script type="text/javascript">
var dp = new DayPilot.Scheduler("dp");
dp.onBeforeEventRender = function(args) {
args.data.areas = [
{
top: 3,
right: 2,
bottom: 9,
width: 17,
onClick: function(args) { dp.events.remove(args.source); },
visibility: "Visible",
css: "event_action_delete"
}
];
};
// ...
dp.init();
</script>
Use visibility: "Visible" to make sure that the icon is always visible.