What are some mental and physical exercises that unblock the throat chakra?

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Sing. Speak your mind. Share some wisdom with someone.

I can't help but feel that these are the outcomes of having an open throat chakra, rather than ways to achieve one. But it must be more like the muscle that has to be worked, and a muscle allows for stronger usage of that muscle.

I would say that is part of it. It's a process.

As Nau7ik mentioned a lot of times blue ray blockages are rooted in lower ray blockages. For me I have yellow ray issues that lead me to sometimes hold back from participating in social activities or conversations or altering my opinions so I don't cause waves, which ends up leading to blue ray issues.

What if I can't laugh without forcing it? Is that really clearing anything?

Sounds like you would need to work on your orange ray first.