We generalize the optimal knowledge extractor for constant-round special sound protocols presented by Wikström (2018) to a knowledge extractor for the corresponding non-interactive Fiat-Shamir proofs in the random oracle model and give an exact analysis of the extraction error and running time. Relative the interactive case the extraction error and the running time are both asymptotically increased by a multiplicative factor equal to the number of oracle queries made by the prover. Through carefully chosen notation, novel concepts, and a technical lemma, we effectively recast the extraction problem of the notoriously complex non-interactive case to the interactive case. Thus, our approach may be of independent interest.