Interesting question. I'll provide my answer in five parts.
“Taking the liberty”
First of all, there's the notion of taking the liberty to do something. It doesn't sound wrong, but it doesn't sound contemporary, either. I looked for usages in Google books, and found plenty of hits, but most were in more antiquated contexts. So I went to Ngrams, and found this very interesting result:
I asked myself, "If 'I took the liberty to disagree' sounds old fashioned, what would I say today?" The first thing I thought of was:
I have the right to disagree.
which yields another interesting Ngram:
It looks to me like, as talk of "taking liberties" waned, talk about "having rights" was on the rise – at least from an English perspective.
“Venturing to disagree”
Then there's your question about venture. The phrase venture to disagree suits me just fine, particularly when you want to emphasize that a little disagreement might be surprising. (I think dare to disagree might be more appropriate in more dangerous circumstances; in other words, I might venture to disagree with a coworker, but dare to disagree with a dictator).
Providing context in a question
In any case, I'd venture to say that main reason your phrases "sound incorrect" is that you didn't provide ample context to let them sound correct.
Consider this example:
I want to remind you that...
Is that something a native speaker would say? Does it sound right, or wrong?
Truth be told, it's hard to say for sure, because we have so little to go on. Look what happens when I set a context instead:
Suppose a group of teenagers are causing a commotion at the library. The librarian approaches them, and says:
I want to remind you that we expect patrons to be quiet in a library.
Is that acceptable English?
With the additional context, the question becomes much easier to analyze and answer.
“Venture to Say”
Now, back to your example:
I venture to say that...
Does that sound acceptable, or awkward? Well, I don't think I would ever say to my friend at a rugby match:
I venture to say that the home team is having trouble moving the ball.
(That sounds too stilted for the rugby stands). However, I might say to my boss:
I was a little nervous giving bad news to the manager, but I ventured to hint that the project might not be on-time.
I would like to venture that...
That one sounds off. You could say:
I would like to say that our research might be going in the wrong direction.
I would venture that our research might be going in the wrong direction.
but "would like to venture" seems like too many layers of indirectness.
Lastly, a quote from NOAD:
venture (v.) 1. dare to do something or go somewhere that may be dangerous or unpleasant
2. dare to do or say something that may be considered audacious (often used as a polite expression of hesitation or apology)
Context is everything. Check the meaning, check published usages. Then, if the word fits, venture to use it.