This quite an interesting conundrum. I'm hard pressed to think of any restaurants that don't use eggs apart from some vegan places. But, ironically, most street food falls into this category... just maybe steer clear of malatang; a friend told me last night that a lot of those places use recycled oil. which contains far worse contaminants than eggs.

Alternatively, if you focus on the higher end of the spectrum (restaurants with foreign owners/chefs), you should be okay.