A thumb drive has the benefit of not requiring an internet connection so it’s got that going for it.
There shouldn’t be any “temporary” links to reference files. The references should be linked to files in folders other than temporary files. Most likely in some project folder on your computer. Links to temporary files can and will become corrupted when the operating system does maintenance. If you aren’t linking to non-temporary file locations, you should unlink and embed the files into the LayOut file so that LayOut won’t go hunting for those temporary files.
FWIW, the LayOut file includes copies of any reference files you have inserted in the project or that may be included in your template. That includes SketchUp files as well as text files, spreadsheets, images, and CAD files. This makes it so you don’t need to include copies of those files with the LO file just to be able to work on the LO file elsewhere. As mentioned before, though, it means that if you edit the embedded version of the file, it will no longer match the original.
If you are going to use a memory stick for moving your files, you might just plan to keep a project folder that includes the original reference files and copy that whole thing to the memory stick. If you make changes to it away from your office, you can just replace the old files with the updated ones when you get back.