That feature is (as far as I'm aware) usually called Reverse Stereo.
From a little searching, it seems that there's no native way to do this in Windows XP or Vista.
Your best bet is probably to go to the website of the Manufacturer of your Sound Card/Chip, and to look for different drivers and/or a utility that can give you extra control over your audio device.
Other than that the only option seems to be to get an extension cable and put the speakers back on the proper sides of the monitor.
It does sound like an interesting project, a system-wide audio filter.. but that's completely over my head and out of my league, not to mention the time it'd probably take to implement something like that.
Pre-post Edit:This webpage here
has a suggestion. What it seems to consist of, is 2 short extension cables and two stereo splitters.
Assuming you don't want to solder one up, you can do it with two 1/8th-inch-plug to twin-RCA-plug adapters, two RCA cable joiners (female sockets at both ends), and one 1/8th-inch cable joiner (female socket at both ends). Plug one adapter cable into the speaker output, attach an RCA joiner to each of its plugs, plug the RCA plugs of the other adapter cable into the joiners (with right going to left and left going to right; this is what swaps the sides), then attach the 1/8th inch joiner to the 1/8th inch plug on the end of the second adapter cable. Plug the headphones into the joiner.
All this isn't terribly elegant, but it's not too hideous or stunningly expensive, and it'll give you a few more metres of headphone cable, in case you need it.