I had a similar request a few years ago and didn't find a solution.
I am curious if someone managed to solve this. Guess the problem is, you can't connect the Nintex Forms Web Part to another Web Part.
My approach then was, to use a "Liste item" or "List View" control but there I can't set the mode to "Edit Mode".
it is possible, but you have to have on the same page List View web part of the same list and have configured connection between the two web parts.
then list form web part shows an item selected in list view one.
when you will have configured that and examine URL, you will notice that there is appended a token &SelectedID=12345 which tells list form web part which item to show.
so you should be able to build a link in mail notification that opens directly a specific item.