"Das will ich nicht hoffen" is the most usual way of saying it in German, considered to be more elegant than "Das hoffe ich nicht."
"Das will ich nicht wünschen" is technically correct, but sounds a bit like somebody not being able to think of the right word. As a translation of "I hope not" it is definitely second choice. (If at all)
But you can say: "Das würde ich niemandem wünschen" or "Das würde ich niemandem wünschen wollen" with the meaning: "I wouldn't wish this to anybody." In this case you are talking about something seriously bad, whereas "Das will ich nicht hoffen" can be something quite harmless.
Isn't it funny how DL does manage to miss the natural expression in BOTH languages? I wonder how they do it.
"Das wünsche ich nicht" is something totally different: "This is not my wish!"
I translated literally "I don't want to wish that" and was marked correct.
It is a comfort indeed, but I always wish a confirmation from DLs' friends... I translated like immolatrix Is it too literal? (I'm beginner in English too).
If "ich will"="i want" why isn't this included in the sentence. The solution corresponds better to "ich wünsche das nicht" i guess.
I've listened to this several times, and every time it sounds like 'münschen' with an 'M'.