Note that some printing systems keep a copy of what they print. I know mine tends to do that -- it is a PC running CUPS, linked to a USB-only laser printer (it turns the USB-only printer into a network printer, but the files to print must go through a spool directory on the PC, as so many files).
So, if your data is that sensitive, then you should not print it at work (it may be safe, but it requires some rather thorough knowledge of the local network configuration to ascertain that).
As for having files which evade an automatic backup system, then it all depends on what the automatic backup system automatically backs up. @Polynomial's suggestion of using a USB stick is sound -- if you can assume that the backup system is "sanely configured". I would not wage much on that, personally.
(If you have administrator/root rights on your desktop system at work, you could install a VM like VirtualBox, within which you could make a basic Linux installation, and, in that Linux system, create a RAM disk into which you would be able to deposit your precious files, and then have a look at them. This should avoid unwanted copies. But that's a bit extreme and does not solve the printing problem.)