API Gateway is a way to deploy your API to production, not to host API docs. If you want to easily host your interactive Swagger UI, you could try deploying your API also to EC2 instance, ECS container or by leveraging some platform designed for hosting things like API docs such as readthedocs or heroku. Hope that helps!

Data Engineer, M.Sc. in BI, AWS Certified Solution Architect, HIIT, cloud & tech enthusiast living in Berlin. www.annageller.com