Looking at the list of fallacies you quote, I would say this is not possible — most of them have got nothing to do with the language itself, but with the way it is used. It's a bit like making a kitchen knife that you cannot use to hurt someone with.
The Fallacy of Composition is related to reasoning. I cannot think of any way that a language can make that impossible. As long as you have expressive power in the language to express anything, you can express incorrect reasoning as well. The same goes for False Attribution, which is about how you use language, not anything in the language itself.
Loki's Wager refers to the absence of clear definitions or boundaries. The world is not clear-cut, so language cannot be like that either. Defining where the head starts and the neck ends is unrelated to language. Unless you want to accompany each word in that language with a book that defines exactly what it means.
Even the Fallacy of Accent is a problem, unless you take stress patterns out of the language, which then is a lot less usable, as stress is a good way of expressing nuances of meaning.
Syntactic ambiguity is about the only one which could be avoided through careful language design. But most 'usable' languages have some of that as well, especially if they are reasonably complex.
Most of these verbal fallacies are to do with the way you use language and express meanings, which you could do in any language. Syntactic ambiguities crop up more often than you would think, but unless you are a linguist, you won't even notice most of them, as it is usually very clear which meaning is the appropriate one in the context.
So, my answer is no, because it is not even possible to do that.