How to use two Integration types in AWS API Gateway?

API Gateway allows two integrations types for HTTP endpoint HTTP proxy integration or the HTTP custom integration. You can use any of them. https://docs.aws.amazon.com/apigateway/latest/developerguide/setup-http-integrations.html

If your use case requires only a token to be sent to backend HTTP endpoint, with proxy integration API Gateway passes the client-submitted method request to the backend. The request data that is passed through includes the request headers, query string parameters, URL path variables, and payload.

If you have a specific requirement to modify client submitted data, you can achieve your use case with HTTP custom integration as well as with a Lambda function in between to send requests to backend.

https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-create-api-as-simple-proxy-for-http.html