Is is possible to oit the egg yolk?

It might be possible to omit the egg yolk, which is there as an emulsifier for the Caesar dressing. You could try using aquafaba (cooking liquid from chickpeas, that water in canned chickpeas) or use can use a milk mayonnaise (David Leite has a recipe on his website, Leite's Culinaria).

We should probably wait for Mr. Kim to chime in, but you might be able to use regular or vegan mayo instead of the egg.