It's pretty easy to deduce someone's work email address. If you have the recruiter's email, you could work out the pattern to email the CMO directly.
As opposed to the other two answers, I see the thank you note as a very valuable tool for a few reasons:
1) Showing appreciation is a good thing (however, LinkedIn is not always the right method of communication)
2) It reminds the interviewer about you and gets them thinking about you as a candidate
3) You can use that thank you letter to remind them why you're the right candidate. Thank them for the interesting conversation about "X" and how your experience with "Y" can directly help solve the problem they have with "X".
Another option, if you can't track down the email, albeit slower, is to send a thank you note to the office addressed to the CMO.
Best of luck,
— Ask Tigress