Tiny Core uses desktop files. Load the extension and check out /tmp/tcloop. For example, the desktop file for Dillo in dCore when mounted is /tmp/tcloop/dillo/usr/share/applications/dillo.desktop. You could unpack the .tcz, modify the desktop file for your preference and repack for use.
Easier just create a custom menu entry, if your Window Manager supports this.
Or if you keep the extension in OnDemand, modify the OnDemand script. With OnDemand improvements, the same applicaition can be launched repeatedly from OnDemand menu during the same session without difficulty. For example, modifying Dillo to open Google when launched from the OnDemand menu:
ondemand -e dillo.sce www.google.com