The words "cheer up" themselves aren't offensive but the idea of a stranger telling me how to feel is.
Someone telling me to keep my chin up is someone encouraging me. Someone telling me to "cheer up" is telling me I have no right to feel sad. That's how I would interpret it. (Granted, I am a bit sensitive to this. I really get annoyed when people tell me how I should feel.)
I say si-chew-ay-shun and in-fa-chew-ay-shun.
Student or Learner