The definition you linked to includes two definitions of cynical, apparently from Collins English Dictionary
And it is true that people are often described as cynical when they are "showing contempt for accepted standards of honesty or morality by one's actions," as in the case of the politician you described.
However, usually, when one is referred to as a cynic (noun) in contemporary English, it means that they qualify for this definition, per the OED:
A person disposed to rail or find fault; now usually: One who shows a disposition to disbelieve in the sincerity or goodness of human motives and actions, and is wont to express this by sneers and sarcasms; a sneering fault-finder.
Based on usage, one might refer to someone like the politician you described with the adjective "cynical," but would be less likely to call them the noun "cynic." When the noun "cynic" is invoked, it usually applies to someone like yourself in this situation, who "disbelieve[s] in the sincerity or goodness of human motives and actions," as opposed to someone who "shows contempt for... standards of... morality."
If you want to give yourself some credit for holding these views about a particular politician and not people in general, you might not refer to yourself as a cynic but rather a skeptic.