Firstly you can set the label text to very small with a very small font and try to mend its color with the background. These options appear on configure desktop window. But still there will be some small line type thing left under it.
You can use script to completely remove the labels.
Create a background image set it as a container layer. Then create a child object with the dimensions you want the shortcuts to have and give it a name. Now set its position so that it gets invisible means something like -20 and -50. The script will be something like this...

Sub Object_ondropfiles(f)
msgbox "Click Ok to have a shortcut"
For Each elem In DesktopX.Object("background object name").Children
DesktopX.object.("child object name").picture = elem.picture
DesktopX.object.("child object name").command = elem.command
elem.delete
Next
Object.clone("child object name") "child1" posX, posY
End Sub

On dropfiles firstly there should be a check if there are multiple files dropped or only one. It only works for a single file drop. It cant work for jpeg, bmps cause there will be a menu on the drop of these file. but this can be partially solved by firstly checking the extension of file dropped.
You can have many shortcuts alighed by setting posX=DesktopX.object("child" & Right(Object.Name,Len(Object.Name)-5)-1)+ gap.

I know that I've written it in alot confusing way but I hope this will provide you atlest some help.

Yes, I appreciate your scripting Haptork. But I was hoping for a one click solution, to be part of DX, done by the DX programmers. I need a one-click, global solution. One at a time is way to slow and tedious. I am hoping for this to become an update to DesktopX in the next version? Set 1 setting, and it applies to all labels. It could adjust transparency, or color. Magic pink works well, but one at a time does not.

I am correcting the code lines I wrote. These lines are useful if you want to control the shortcut objects. If you want the labels to hide universally for a dxtheme then the reply#4 will do it.

Sub Object_OnDropFiles(f)
For Each elem In object.Children
If elem.name = "" Then
elem.name = "dxico"
End If
Next
End If
DesktopX.Object("child object name").clone "clone1", posX, posY
DesktopX.Object("clone1").picture = DesktopX.Object("dxico").picture
DesktopX.Object(clone1).command = DesktopX.Object("dxico").command
DesktopX.Object("dxico").delete
End Sub

Now why didn't I think of that? (jk)
Thanks for this handy tip!

It works until you turn it into a widget.  (