If you did not utter the words of oath then taubah and istighfar is enough for breaking the promise, monetary kaffarah is not wajib in this case. Yes, if you give something in charity then there is no problem rather it is better. As it is mentioned in hadith that sadaqah removes the anger of Almighty Allah. If the organization is trustworthy then you can pay to it as well.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband