If Jim uses Shrivelling to attack, and draws a skull token, his ability changes that token to a value of 0, however, does he still take 1 horror for drawing it do perform the test?

yes. Jim's ability doesnt change the token to a 0, it changes the modifier to 0. He still drew the skull, so anything that triggers off of drawing the skull still triggers, including Shriveling's disadvantage. Other affects of the skull token that aren't negative modifiers (such as draw another chaos token, popular in some scenarios) also trigger.

1 minute ago, awp832 said:

yes. Jim's ability doesnt change the token to a 0, it changes the modifier to 0. He still drew the skull, so anything that triggers off of drawing the skull still triggers, including Shriveling's disadvantage. Other affects of the skull token that aren't negative modifiers (such as draw another chaos token, popular in some scenarios) also trigger.

ok, this is what i suspected. thanks!