I work in the sales department selling CV writing service. Do you think that it's risky to advertise it on Facebook without telling my Manager?

will be better through official facebook of your Dept or client

Advertising it isn't a problem infact it is a necessity to its success but what matters here is doing it officially after consultations and advice from your manager or superior, this will ultimately leave no chance to misunderstandings, conflicts or contentions which might otherwise turn out badly for you and your career ( risk of punishment). Thanx for the invitation