Ask your client for more info about image size, because only specifying 300 ppi isn't enough. It's like telling you to get in your car and drive at 60 mph. How long? How far? Get either pixel dimensions or print (layout) dimensions. And ask them which CMYK profile. There are dozens.
Absolutely correct. At the very least, you need to know the basic press conditions -- web or sheet fed, coated or uncoated paper. If they can tell you that, you can use Convert to Profile in Photoshop, choose the appropriate profile (eg., U.S. Sheetfed Coated v2) as the Destination Space, and Relative Colormetric (or possibly Perceptual) as the rendering intent. Provide the full native file -- the pixel dimensions that came from your camera -- and set the resolution to 300 pixels per inch. (You can choose this when you export the file to Photoshop.)
(If they can't tell you the press conditions, you can't provide a CMYK conversion. You just can't. Provide a file in the sRGB color space and let them have their press people do the conversion. sRGB because that's the color space least likely to get screwed up by idiots.)