I want to make gnocchi without eggs.
Just leave out the egg and use a little bit more potato. I've made vegan gnocchi several times and that's all I did. The starch in the potato will be enough to bind everything together.
My Tuscan neighbor, who made gnocchi every Sunday for about 70 years, never used egg--just potato and enough flour to hold it together. And a plain tomato sauce on top.