Do I Have to Use Raw Eggs? Is there any way to make this without the raw eggs in the cream?

Another option for you would be to use dried egg yolks and egg whites. The process to dry those basically involves pasteurization, so they would be safe alternatives to fresh, raw eggs. If you are willing, you can also safely pasteurize whole in shell eggs at home for yourself. It takes time, but it's easy enough to do if you are of a mind to. And in some localities you can buy eggs already pasteurized as well.

Jo - no, you don't have to use eggs. See this recipe and use it to help you modify the gluten-free tiramisu you linked to your question.
https://www.thepetitecook.com/classic-tiramisu-without-eggs/