A photocopy of every one of your submitted transcripts is included with your LSDAS report.
The report is rather lengthy, mind you, so it is not as if every school out there will have the time to comb through everyone's file.
In my own opinion, I'd say that your GPA is more important at this stage than your transcript. Drop the class and enjoy your holiday.
Then, when you get your grades in, mail off a letter to the school including a list of the classes you took as well as the grades you earned in each of those classes (DO NOT include the details about your dropped class).
You have the option to update your LSDAS report by sending in your most recent transcript, but don't do it until late Feb./early Mar.
Make sure you get that letter out in January though, because it will pacify their curiosity about your grades.
I know that some people may criticise this advice, but it is the best advice that I can personally give you. Just be totally honest about the grades that you do have, and remember that omitting information is not unethical. Not mentioning the fact that you dropped a class is not an issue, because you were never given a grade for that class.