Are any of those files 4GB or larger? That's the typical limit for the FAT file system used on USB keys. If so, you can use a tool like
7-Zip Portable to create a multi-part archive
- use the option to split it in to chunks of a manageable size e.g 100MB.
- select "Store" (i.e. no compression) to speed the process up - you have plenty of space.
You can keep 7-Zip Portable on the USB key to reassemble it at the other end.