Today we introduced a custom domain feature that will allow using your domain or subdomain for all external links for Projects and Events. So instead https://youengage.me/p/project_code you can setup links for Projects to be like https://yourdomain.com/p/project_code or https://yourdomain/e/event_code for Events.
Of course, there is also an option to setup not only top-level domains but also subdomains so it can be for example https://forms.yourdomain.com/p/project_code.