color - How accurate is pantone conversion in Illustrator and how should I send "Pantone References" asked by the printer?

I've been hired to do a big campaign that requires all sorts of permutations of an Illustrator design.

Most recently, I was asked to make a banner. The printer wants my Illustrator file (no pdf) in CMYK, but requires Pantone references. But I have no Pantone Book (and I'm basically too poor to buy one right now).

So I just converted the nine main colors in my artwork from CMYK to Pantone through Illustrators color books. How accurate will this be as a reference for the printer? And is it enough to just use my nine most used colors (there are about 100 colors in my illustration)?

And this might seem like a silly question: but how do I send them this? Do I just add a Pantone Swatches Folder within my file for them? Or do I send this in a seperate file?

I've never encountered these sort of printer requirements and I'm at a loss.

Thanks in advance.