### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

We are using the `Authorization` header for routing purposes

```
 "authorization: AWS4-HMAC-SHA256 <...>"
```

https://github.com/localstack/localstack/issues/5770

### Expected Behavior

Use a custom header to avoid causing confusion with backend integrations

### How are you starting LocalStack?

With a `docker run` command

### Steps To Reproduce

Run a custom HTTP integration without authorisation

### Environment

```markdown
- OS: 
- LocalStack:
```


### Anything else?

No
invocation_context.stage_variables = helpers.get_stage_variables(invocation_context)
                integration_response = SnsIntegration().invoke(invocation_context)
                return apply_request_response_templates(
                    integration_response, response_templates, content_type=APPLICATION_JSON
                )
        raise Exception(
            'API Gateway AWS integration action URI "%s", method "%s" not yet implemented'
            % (uri, method)
        )
    elif integration_type == "AWS_PROXY":
        if uri.startswith("arn:aws:apigateway:") and ":dynamodb:action" in uri:
            
            table_name = uri.split(":dynamodb:action")[1].split("&Table=")[1]
            action = uri.split(":dynamodb:action")[1].split("&Table=")[0]
            if "PutItem" in action and method == "PUT":
                response_template = response_templates.get("application/json")
                if response_template is None:
                    msg = "Invalid response template defined in integration response."
                    LOG.info("%s Existing: %s", msg, response_templates)
                    return make_error_response(msg, 404)
                response_template = json.loads(response_template)
                if response_template["TableName"] != table_name:
                    msg = "Invalid table name specified in integration response template."
                    return make_error_response(msg, 404)
                dynamo_client = aws_stack.connect_to_resource("dynamodb")
                table = dynamo_client.Table(table_name)
                event_data = {}
                data_dict = json.loads(data)
                for key, _ in response_template["Item"].items():
                    event_data[key] = data_dict[key]