Windows Movie Maker will do what you are wanting. It is also capable of compressing the movie file (at loss of quality) so it doesn't take as much space on the thumb drive. Quality of the playback may not even be noticeable on most screens so it would be worth experimenting to find the level that you or your audience are satisfied with.
Be forewarned though, that a hi-quality video file is large and will take a considerable amount of time to process before you get to the saving part. If you are using an Intel I3 processor with a mechanical HDD and 8 gigs of RAM, you are talking hours before you are ready to compress and save.Good Luck.