I am sending digital files to the offset printer who will convert the digital rgb images into cmyk.
If not for this project then certainly for the next you'd be best served by doing the RGB-CMYK conversions yourself. There's much more of an art to it than going Image>Mode>CMYK. You can decide on the best rendering intent for the conversion of each image and just as importantly, then edit the CMYK image to determine how the out of gamut colors will appear. There is no right or wrong, hard fast rule or formula for wrangling out of gamut information (it could be hue, saturation , brightness, or some combination of all three that's beyond the press capabilities), though there are preferred practices to diagnosing and addressing the issue. In short, the RGB>CMYK conversion involves very subjective decisions and passing them off to someone else will invariably lead to different results than you may have desired. It's not just "I can't have that saturated green or dark blue on press", it's what you choose to replace it with that can really make the difference on the printed page. Having recently finished a book where I had to convert almost 300 images individually, I can say that the effort was well worth it in the end. Sure, a fair number of the images looked OK with a straight conversion, but many others would have been disastrous without some individual adjustments.
Plus, by sending RGB files you're giving the printer lots of colors he has no
chance of being able to print. Typically, this will not make him happy. And nothing will come close to looking like your RGB inkjet proofs. Typically, this will not make you happy. At the very least you may want to consider using the PS proof option when making your proofs so that your inkjet simulates the press behavior.