You should be able to pass the event id to the modal dialog like this:
<DayPilot:DayPilotScheduler 
    ID="DayPilotScheduler1" 
    runat="server" 
    EventClickHandling="JavaScript"        
    EventClickJavaScript="eventClick(e);"
    ...
    />
<script>
    function eventClick(e) {
        new DayPilot.Modal().showUrl("Edit.aspx?id=" + e.id());
    }
</script>
The EventClickJavaScript event handler receives the event object (DayPilot.Event) as "e". You can get the event id by calling e.id().
Please let me know if it doesn't work as expected.