This is a better tested version:
Sub UnMergeCopy()
Selection.MergeCells = False
On Error Resume Next
If Selection.Columns.Count 1 Then
Selection.FillRight
End If
If Selection.Rows.Count 1 Then
Selection.FillDown
End If
End Sub


Also, can I assign a key in the code itself?

If you mean assigning a hot key: Tools/Macro (or Alt-F8) / Others
(bottom-right button

Finally, without going through conniptions with assigning security can I set
it so that it runs the macro in any sheet I bring up?

This macro does run in any sheet!

Regards,
Stefi