"Do not wait until Thursday" is not only a correct translation, it is better English.
I think that would be עד יום חמישי
If your exam is on Friday, don't wait until Thursday to start studying. If this is the intent in Hebrew, then "until" would make better sense in English.
"Don't wait for Thursday" is perfectly correct English in some contexts. For example if there is an implied event on Thursday, such as a birthday: "My family is in danger so don't wait for Thursday to buy me a new can of owl repellent"
"אַל תְּחַכּוּ לְיוֹם חֲמִישִׁי!"