You're on the right track, perhaps, but caught the wrong train.

Cream of tartar is associated with eggs, but only as an acid used sparingly to mysteriously increase the loft and stability of an egg-white foam, such as a meringue or mousse. Cream of tartar is in no way a replacement for the egg itself.

If, for the sake of food safety, you want to use a pasteurized product, choose either dried egg white and reconstitute it, or pasteurized fresh eggs, which you may be able to find at your grocery store.