"negative" and "black and white" are not synonyms.
Many companies have a 1-color version of their logo for things like cardboard boxes and any collateral where it is a waste of money to print more colors. It may not be used often.
However, it sounds like you are asking whether you can or should do it. The answer is: in general you are free to do whatever you want and they are free to complain about it.
One might argue that it is their property, but you probably have a fair use case considering it is for self promotion and it is specifically tied to your employment history, and you are altering them (original derivative work).
If there is going to be a problem it will be with the use of the logo at all and not an "unapproved" style faux pas.