@greyknight USB is the least likely to be detected and easiest. If you're exporting an entire DB, that's going to be very noticeable over the network unless you're going to do a lot of work obfuscating traffic.

Depending on how quickly you need to move thing, I'd do a test run with a USB moving something non-critical, wait a week or so and see if you get a visit from security. If nothing happens, go for the transfer.

If you have a disk drive, burning a CD may be an option, too.