I'm afraid not, perhaps this would be more natural:
I don't want to do this.
I don't want to do this task.
I don't wanna do this task.
Your sentence is following the Japanese grammatical structure of [task] wo yaritakunai desu but we don't use this structure, instead we always consider the full sentence eg [watashi wa task wo yaritakunai desu] and then we simply say [I don't want to do this task]. The order of what we say is different to Japanese, plus it is important for English speakers to include the subject (I, watashi) in all of our sentences.