If you controlled this application, you can use the externally_connectableproperty and listen to requests to launch the application.
But it looks like you are not in control of this application. The normal code of a webpage is unprivileged and cannot name chrome-extension://URLs, etc.
Perhaps you can make an extension to the launcher. Using the managementAPI , you can launch the application using
chrome.management.launchApp("cnciopoikihiagdjbjpnocolokfelagl");
and this can again be called via messaging over the Internet with externally_connectable. But this obviously requires that your users have two different Chrome add-ons installed, the corresponding application and your control panel.