Can't you simply remove the unwanted button from the toolbar in the layout > formview > child panel settings?
Perhaps I'm not sure what you need here.
Unfortunately, both buttons "New Attachment" and "New URL" are automatically displayed by Ivanti if I just add the single "New Record" or "New Record Menu" button to the "Attachments" toolbar, Thus, I have only one button defined in child panel settings but two buttons are displayed. And not surprisngly, if I remove the button in the child panel settings, both buttons "disappear":
Sorry, I didn't realize the two buttons weren't exposed separately on the AdminUI. That being the case I think this is a special are where that pair of buttons is hardcoded. I'm not sure if this can be done in ISM at this time. You could easily make a custom BO that you display in place of the Attachment child panel that has a similar setup and only accepts URL entries. All you'd really need is a single long text field to store the URL in and then make it clickable on the grid.
Would that approach make sense? If not you may need to log a feature request with PM to see if they are willing to break up those two buttons and make them both available on the AdminUI to be configured.