### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

APiGateway Model that being created by CDK project stores the JSON schema with a single quotes instead of double quotes which leading to an error in parsing this json object. 

you can refere to this article to see the steps 

https://dev.to/dvddpl/reduce-lambda-invocations-and-code-boilerplate-by-adding-a-json-schema-validator-to-your-api-gateway-15af

and it works fine on AWS account 

also you can look on the attached image how localstack stores the JSON object with a single quotes, I tried to edit it manually through UI but it return it back with single quotes

![Screen Shot 2022-10-18 at 4 28 08 PM](https://user-images.githubusercontent.com/106184681/196769273-0834865a-2fb3-4efc-b3a9-9da6b2ad511d.png)

### Expected Behavior

store the json schema in correct JSON format

### How are you starting LocalStack?

With the `localstack` script

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command, arguments, or `docker-compose.yml`)

    localstack start

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

    cdklocal deploy


### Environment

```markdown
- OS:OSX
- LocalStack: 1.0.4
```


### Anything else?

_No response_
snapshot.add_transformer(snapshot.transform.key_value("cacheNamespace"))
    stack = deploy_cfn_template(
        template_path=os.path.join(
            os.path.dirname(__file__), "../../templates/apigateway_integration_no_authorizer.yml"
        ),
        max_wait=120,
    )
    snapshot.add_transformer(snapshot.transform.cloudformation_api())
    snapshot.add_transformer(snapshot.transform.apigateway_api())
    snapshot.add_transformer(snapshot.transform.regex(stack.stack_name, "stack-name"))
    rest_api_id = stack.outputs["RestApiId"]
    rest_api = aws_client.apigateway.get_rest_api(restApiId=rest_api_id)
    snapshot.match("rest_api", rest_api)
    resource_id = stack.outputs["ResourceId"]
    method = aws_client.apigateway.get_method(
        restApiId=rest_api_id, resourceId=resource_id, httpMethod="GET"
    )
    snapshot.match("method", method)
    
@pytest.mark.aws_validated
@pytest.mark.skip_snapshot_verify(
    paths=[
        "$.resources.items..resourceMethods.GET"  
    ]
)
def test_cfn_deploy_apigateway_from_s3_swagger(