Have you considered sending a webform saying something along the lines of "this is to notify you of the change of employment of Mrs razor787. Employment A terminated on <date>, employment B commenced on <date>". This way you would have notified them, and it would be up to them to ask for further information if they want it, but you would have been upfront and honest with them about the change of circumstances.
I wouldn't offer up an updated copy of the labour book, but would be prepared to provide it if they ask for it at a later date. In the end of the day I don't believe it makes any sense for IRCC to ask for an updated labour book as your wife is not an EE applicant (and not an economic migrant in general), her employment history or education is of little relevance here.
Yeah, I guess I will have to. But it is a bit worrying if they ask for the workbook copy. She might not keep the job if they find out she's moving out of the country.