I have never tried this recipe, so I can’t promise anything. With that being said, I have heard great things about aqua faba (chickpea liquid) being a great substitute for eggs. You could do a test run and see if it works for you.
https://geekycakes.com/2015/05/08/egg-free-dairy-free-vegan-italian-meringue-buttercream/amp/
Good luck! Sorry I couldn’t be of more help.
