Underscore is not recommended for headers.

But since you can’t modify your client request, accept access_token as is in method request and modify it via integration request using integration request headers.

https://docs.aws.amazon.com/apigateway/latest/developerguide/request-response-data-mappings.html#request-response-data-mappings-example-2

This way, you can accept the access_token value sent by client and map it to access-token before sending it to your service endpoint.