Here is a bit of a contrarian idea. If you are certain that the memory stick is the most current, simply use the RM-to-go procedure to copy (sync) it back to your C: drive and don't lose any sleep over it.
I used to use Rm-to-go very heavily, indeed on a daily basis. I used it between two computers that I owned rather than at a library, but the principle is the same. There were occasions every couple of months or so where the sync process would report a timestamp conflict. In these situations, I was 100% certain that I had not made a procedural error in using the product. For example, you need to be sure that you have the hard disk version of RM completely shutdown before you run the RM-to-go sync procedure and that you never start the RM-to-go version of RM again - not even to look at the file - until you have completed the reverse sync from the memory stick back to the hard disk.
I checked everything I could think of very carefully such as the clock and time zone settings on both computers, but I could never pin down a problem that was repeatable enough that I could actually report it to the RM Helpdesk for resolution. I do know that a potential issue is that memory sticks usually do not use exactly the same file format as does a hard disk, or at least they didn't use to. And the clock resolution of time stamps on a memory stick were not as accurate as was the clock resolution of time stamps on a hard disk. But this shouldn't be a problem because we are only talking about a difference of a second or two. But nevertheless I always wondered if there might be a problem in Windows somewhere with the timestamps it was putting on files. The best I can tell, RM-to-go does not use its own timestamps or other verification methods. And indeed, Windows timestamps are quite a mess, what with different time zones to consider, what with daylight savings time to consider, and what with different file formats to consider. I think RM-to-go relies 100% on the Windows timestamps in the file system. But to tell you the truth, I'm not sure exactly how it works.