I know you specified a lack of food, but I need to give a complete explanation of the differences in order for it to all make sense.
Depending on usage, it may or may not be appropriate to add up. While it's generally true that up is used metaphorically and something without it is taken literally, that is not always the case.
From Merriam-Webster's definition of cook up:
1 : to prepare (food) for eating especially quickly • I can cook up some hamburgers. • He cooked this whole meal up in less than 30 minutes.
2 : to invent (something, such as an idea, excuse, etc.) to deal with a particular situation • They cooked up a scheme to fool their neighbor. • You'll have to cook an excuse up quickly.
Also, its definition of just cook:
2 : to prepare for eating by a heating process
3 : falsify, doctor
- cooked the books with phony spending cuts and accounting gimmickry —Colleen O'Connor
4 : to subject to the action of heat or fire
In terms of the kitchen-based activity, there is a subtle distinction.
I'm going to cook dinner.
This refers simply to the act of mixing, baking, or otherwise preparing the ingredients that make up dinner.
I'm going to cook up dinner.
While it can mean the same thing, it's similar to saying, "I'm going to whip up dinner." It has a sense of quickness or triviality. It would be more common to hear, "Let me just cook up some dinner" than it would be to hear "Let me just cook dinner". (Unless a distinction is being made between eating in and going out or ordering in.)
Your example sentence, without further context, is ambiguous.
If she is standing in front of him with a chef's apron and a mixing bowl, either cook or cook up would be appropriate.
If she's holding a match in one hand and a non-food substance in the other, then it's likely just cook that should be used.
If the context of the conversation is such that it seems she's concocting some plan (rather than there being anything to do with food or fire), than it's likely that cook up should be used. Barring, of course, the exception that she's considering falsifying a written record, in which case just cook could be used.
Given the possibilities, it's more likely (although not a given) that you do want to use cook up.