I don't see how you would be able to disable those tray icons unless the application that they represent supports it. However, if they do, it is likely a setting in the registry or something, which you can set with DA.
If you are referring to DA's own tray icons, I can help you with that.
DA has, I believe, at max, three tray icons, the DA Agent, the DA Remote Agent, and the USB/Port Security icon. If I am missing any, my apologies.
The DA Agent icon can be disabled in Global Options > Desktop Agent. The USB/Port security icon and the remote management icons can both be disabled in the actual elements where you deployed them.
Hope this helps.
Regards,
Jack Doyle, Systems Engineer
ScriptLogic Corporation
http://www.scriptlogic.com