Removing hotkey F1 from command HelpIndex is not really possible. The hotkey can be removed in the key mapping configuration from this command, but it has no effect. You can assign only additional hotkeys.
The reason for this behavior is found in the libraries of Windows. Key F1 opens in all "real" Windows applications the context sensitive help. Context sensitive means if a help ID is assigned to the window, command in menu, the dialog, or item in current dialog having the focus and key F1 is pressed, the help page with that ID is opened. If there is no help ID assigned to the item with the focus, the default help page as defined in help file is opened.
For example you can open any dialog in UltraEdit and press key F1 to get the help for this dialog (if there is a help page and correct ID is assigned). It does not matter if the dialog has a button Help or not. You can also open a menu, move the mouse over a command and press key F1 to get the help for this menu command. Some applications support even help for a configuration setting having the focus. (UE shows the help page with all the settings of the current configuration dialog.)
Of course it is possible to override this standard feature of Windows applications, but that requires additional code within the application. The developers of UltraEdit have not added obviously such a code to source of UltraEdit.