A person is a radical skeptic if and only if that person believes that knowledge is impossible to attain.
That is not a skeptical position, which would withold judgement on that.
Unless, you implicitly define 'knowledge' as consisting of provable truths in a way analogous to mathematics, or as emerging from some foundation which somehow resolves the nature and origination of meaning. These are we think we have strong evidence, not possible.
Science is tentative and proceeds only by hypothesees. It has been argued, that science must remain fundamentally incomplete, that is if all true axioms are known and unified, all truths will still not be recursively enumerable http://www.hawking.org.uk/godel-and-the-end-of-physics.html
So is science radically skeptic? No, it simply doesn't bother to be. The scientific positiin is agnosticism, not atheism, because the metaphysical speculation is just irrelevant without relating it to specific evidence.
I know of two well established schools of thought which can reasonably be described as radically sceptical. The first is the Madhyamaka school of Mahayana Buddhism. The acknowledged core of this is the demonstration of the futility of metaphysical speculations.
The second is postmodern antifoundationalism, which is approximately the view that knowledge must be understood with a behavioural context and reference to power, which places fundamental limits on the possibility of objectivity (though it can be achieved by degree). This does not view knowledge as impossible, only redifines it as not having the transcendental qualities which might wish it to have, which are fundamentally revealed as a power-play.
So. Your definition is essentially absurd, self contradictory. Radical skeptics can and do place limits on the definition and especially objectivity or universality of knowledge. It is a perspective widely, and convincingly held, which allow many metaphysical quandaries to be discarded, including whether we can have fundamental or transcendentally true knowledge. The only reason this is not more widely recognised, is that radical skeptics exactly have no interest anymore in whether their view is fundamentally or transcendentally true. Lol