"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.