I"m not sure if you're going to be able to accomplish this particular task, you either can manage widgets or you can't in terms of delete or add, it's hard to do it selectively. An option though is you could have that particular 'widget' not have it's configuration in the widget, but have it act like a repeater that points to a Page on the content tree where the user could edit. So in essence you would make a page type that has your widget configurations, and put the custom logic to pull from there.
then give that user no widget permission (so they can't add/delete) but grant them access to the page.
However i would imagine if they can edit widgets, they are an editor, and you should be able to train them to "don't push that button or don't do this or that" which may be far easier than trying to hard code it in.