I have an app I made a long time ago called Clutterbuster
that could work for this. But it only works with exe files and if the exe file doesn't contain an icon, the button will be blank.
Place it at the root of your Dropbox folder. Set it up by right clicking a button and selecting an exe file to associate with it. Once you have set all the buttons you desire, close the app and it will save the settings in an ini file. Open that ini file in Notepad and edit the paths to be relative.
It will hold a total of 100 apps, but you can use multiple copies if you need more. Just name it something different (ex: Clutterbuster1.exe, Clutterbuster2.exe, etc. or Web Apps.exe, System Utilities.exe, etc.) Each copy will create its own ini file.
Keep in mind that this is no longer being actively developed by me. It is given as-is. If it works for you, great...if it doesn't, delete it and forget I suggested it.
I originally whipped this up to shut my daughter up when we shared a PC with a single user account and she started complaining about all my apps she wasn't interested in cluttering up the taskbar. It was created without writing a single line of code. If you want the Delphi "source" PM me.