The easiest ways to keep the current year's list from being disclosed to a participant are to either not store the list at all, or to have the administrator of the selection process not participate in the gift exchange.

If you have a small enough office that you can get everyone to let you know whose name they had after the exchange, you can create this year's list for reference next year after the exchange. Then, you only need to make sure as you select names that you're not repeating, and don't have to store the new selections. Then next year you can collect the list from the participants again. That's a bit of a headache as the number of people involved grows, I understand.

The other option I mentioned, to have the administrator of the selection process not participate, doesn't mean you need an outside company. It just means you, or whoever runs the selection code you write if it's not you, doesn't give or get a present. Your contribution is the code and the operation of the process, for which you get the warm fuzzy feeling of having facilitated the gift exchange for others. Snooping coworkers may still be an issue. ;-)

If neither of these are workable, then BrowserUk's email reminder idea or Fletch's secret sharing idea would both give you a better match. I like the simplicity of BrowserUk's suggestion to use an email reminder system. One can think of it as an automated impartial outside party. The secret sharing idea Fletch proposed has some serious geek cred to it, and should be a novel and fun way to handle things.