That's a good idea, a nice easy way to get a pseudo-random selection, but what about sending them to the correct followup page? That wouldn't work unless... aha! You could pre-select the winners! You could take the entire campaign segment and import them into SQL (or Excel) and set a custom field to 1 for the winners, then upload them back in before the campaign runs.
The problem there is that they have to click on the Easter egg in order to win, and we don't know in advance which prospects will click. So if we pick 10 winners and then some of them don't click, we end up with less than 10. You could select more than 10 winners and assume not all will click, but what if more than 10 of the winners do click?
Oh, one other thought - if the legal department doesn't like selecting winners based on their ID field, you could use a true random process (drawing numbers from a hat) to select the number to compare the ID with - so if you want a 1/100 chance of winning, instead of selecting everyone whose ID ends in 99 as a winner, you pick a number between 0 and 100 from a hat and then pick everyone whose ID ends with that number as a winner. That would be genuinely random and fair.