I've seen "not to worry" used to mean like "Don't worry" sometimes in conversation, so I think I could invent some similar expressions like that like
Not to mind. It gonna be all right. (meaning Don't mind. It gonna be all right.)
Not to be sad. She wouldn't die of cancer like your father. (meaning Don't be sad. She wouldn't die of cancer like your father.)
Not to run at home! (meaning Don't run at home!)
To know whether they sound natural, I asked native speakers about these sentences, but well, they all answered that although "not to worry" sounds natural, those expressions I invented sound very unnatural.
I guess this is just because they are not such expressions in use even though they do make sense, but I have no ideas specifically why.