In the local Juco culinary program I've taken some classes in, they allow students to use (simple) calculators and paper dictionaries, but no electronics besides the calculators. This came up precisely because of the situation the original poster describes: one student said she wanted to use an electronic dictionary, but they discovered that she had either saved (or bought a package containing) some data that students were not allowed to have during the exam.
Before people go into the issue of memory versus comprehension, understand that in a professional kitchen (or anywhere you have to get things ready in a timely manner), one does not have time to look everything up and memorizing recipes or measurement conversion or other data is in fact a measure of progress in a subject.
That said, since most schools only really care about buzzword-compliance and revenue, the OP should probably just allow the students to tell him they completed the course requirements and save them the time of proving it.