As far as I understand, the sentence I would like to say has two different meanings.
It might just tell that you are about to say something that you feel is important, like in a speech that starts with:
First, I would like to say thank you...
In that case, a translation might be:
En premier lieu, je tiens à (vous) dire merci...
The second meaning occurs when something is preventing you to say it.
I would like to say the truth, but I'm not sure it's a good idea.
You can translate that by:
Je voudrais dire la vérité, mais je ne suis pas sûr que ce soit une bonne idée.
This second form might also be used when the first meaning is intended:
En premier lieu, je voudrais vous dire merci...
but the opposite is not true. Je tiens is much less likely to be used with the second meaning.
Depending on the expected meaning, your original sentence might then be translated either by:
Je tiens à dire qu'il a tort1.
Je voudrais dire qu'il a tort.
Finally, je voudrais dire qu'il soit incorrect is not grammatical. There is no place for hypothesis or uncertainty after je voudrais dire.
1 We wouldn't say qu'il est incorrect or qu'il n'est pas correct because that is more likely to mean that he is "rude, inappropriate".*