'Cheer up' to a friend who got his arm broken?

"Cheer up" is mostly used for someone who is sad or has just received bad news. It isn't much used for someone who has been injured, but probably wouldn't be completely wrong.

Just say you hope it heals quickly.

We generally say "cheer up" as a kind of rebuke or encouragement when someone is behaving in a doleful or miserable way. It can be more or less sympathetic, but it is not really a way of comforting them. It can carry a strong implication of "Don't be such a wuss", and is often a way of cajoling someone to act more cheerfully than they might feel like doing.

That native speaker was right.

You could tell them to "Hang in there" as in, "bear up, things will get better soon". I find this to be a useful general encouragement.

People used to say "keep your pecker up" in Britain, but I think that is open to misinterpretation these days, because although 'pecker' means 'nose' in the British saying, it means something different in the USA.

LOL funny

I think that rather than telling him how he should be feeling, let him know that YOU think it's sucks that he broke his arm and if he needs anything that you're there to help out (yard stuff, heavy lifting, chores, whatever).

Generally, people don't like or need to be told how they should be feeling. Telling somebody to "cheer up" basically says "whatever emotions you have about this, they are wrong , and I know how you should be feeling".

Just offer support and acknowledgement​ of the situation and validation to whatever feels this guy has about his broken arm.

Yes. This is absolutely right. You might say "cheer up" etc to someone who has a long face for a comparatively trivial reason, e.g. it is raining on a trip to the beach, or they have a cold, or their football team has lost a match.