I think you need to be very careful.
Are you sure your company doesn't allow senior manger to put such expenses on their credit card as unofficial, and non taxable, perks?
Also, how did you come across the info about your manage? Were you spying on him or did you see his credit card statement as part of your normal work. If the latter it puts you in a stronger position.
If what your manage is doing is definitely against company policy, and you can show you weren't vindictively spying on him, I think you should try a personal approach to an appropriate director. You should say you feel very awkward about approaching him, but have inadvertently come across some information you think he should know about. Just give him enough detail so he can conduct his own investigation, and try and keep everything factual so it doesn't appear that you are out to get your manager. Obviously ask that the conversation be treated as confidential, but keep detailed notes about the discussion in case there is any comeback on you later.
Personally if I was one of your directors I would treat a personal approach far more seriously than an an anonymous email, and respect the person who had the courage to approach me directly about this kind of issue.