RE: my question is Can I override the custom entry order in the shortcode of the widget?
Sorry, there is no way to disable the Custom Entry Order per instance. It is applied globally.
I can not think of a way around it as there are no actions I could hook into to add/remove the custom ordering for specific instances. It does make sense that the recently added and modified widgets should not be affected.
The best I can offer at the moment is that I’ll look into it and see what can be done.