Hi, MJ!
I love this question because I grew up in Cajun Country and even have a Cajun maiden name. With that being said, I don't speak Cajun French; although, I have some relatives who do. I agree with writing it in French. I especially like MKWrites' point about readers being able to google those phrases. My recommendation, which I have a feeling you already plan to do but just in case, is to indicate that the speaker has a Cajun accent or to maybe describe it because as I'm sure you know, Cajun French differs from the French language considerably.
For example, and I use this because you mentioned that Cajun is not a written language, friends I grew up with will use the word "sha" on social media, a common term of endearment (or sometimes an insult), but in French it would be spelled "cher." Would any of my Cajun friends recognize it spelled the French way? I think most of them wouldn't, so some clarifications may be needed. Hope that helps!