Well, it has to go somewhere, and I assume you are planning on taking it off the laptop. (Good plan, but be aware that a good repair tech can recover whatever you have deleted, if they are motivated to do so. That is, after all, part of their job. You will have to go to greater lengths to keep it out of their reach.)
What matters here is not how many videos you have, but how much space they take up. The obvious choice is to back up to a cloud storage service. Microsoft OneDrive, for example, gives you 5gb for free. Google Drive gives you 15 GB for free. You can also look at DropBox (2 GB) and Box (10GB). I think those may be free trials for a limited period of time. At any rate, you may be able to divide your videos between those services and then move them back when you get your laptop.
Of course, with the cloud, you are handing your porn over to a third party. Maybe that bothers you, maybe it doesn't.
If you can spend a little bit of money, you can get a 64gb flash drive these days for under $25. That's a ton more space than you will have with any of the cloud services, and the transfer time will be fast and the videos stay in your control.