"I think, therefore I am."
Though this could fall under this umbrella of the a priori exclusion. I would argue that this is circular reasoning. Your conclusion is that there are no objective truths and your premise excludes a priori knowledge, the literal source of objectives truths. This leads to a valid conclusion. After all, if we exclude the source of objective truths then there are no objective truths. However, the soundness and, honestly, the usefulness of such an argument is questionable at best.
That being said, I think I get what you're getting at. A posteriori knowledge is fallible. It can never be proven 100% correct. This is why theories in sciences, aside from axioms, are never considered hard truths, as science is based in empirical evidence, a form of a posteriori knowledge. I would say that a better way to convey your point isn't to say that objective truths don't exist, or that nothing can be proven real, but instead to say that one must take care in the information they are presenting; that one should be aware of whether their facts are a priori or a posteriori. If the fact is a priori, it's a fact, an objective truth. If the fact is a posteriori then a very large amount of evidence is required to support it and 1 piece of solid evidence against it can falsify it.