Some places offer personal hot pots.
The hot pots generally have choice of chicken broth or spicy stock.

Chicken broth powder (supplied by yourself) could be added to
plain water in the bowl to insure the broth has no egg contaminents.

Fresh meats, poultry, vegetables, seafood, various organs should have no
cross contamination with eggs.

As far as dipping sauce, should not have egg contaminents if you
stick with mixing up your own from soy, sesame, chille, etc.

Dipping sauce pre-made could contain egg.

That's making me hungry for hot pot now, too bad the closest place
is about 50 miles away.