Mobile (mobile number) is more British, cellphone is more American English.
So, sometimes it´s advisable to know your audience and use the word that match it. I mean, if you talk "mobile" to a British person, or somebody that knows this sense of the word, then it´s fine.
Say, if you are in America and when say word, you sense that people around raise eyebrows in that "are you sure of that?" way, then drop it.
My mobile´s 99999-9999 (it´s likely in British English.)
My phone number is 99999-9999 (A faster way, in american English.)
My cellphone number is 99999-9999 (also Ame. English.)
My number is 99999-9999.