How to Helth Check Rest IAM Certificated API

How to health check IAM authenticated REST API using Route53?

I created a Rest API that requires IAM authentication for the API Gate Way. I want to check the health of Rest API. There are 2 options, one is using Route53's health check, and other is cloudwatch Synthetics. I want to use Route 53's health chek if possible because of cost and ease of maintenance.

Is there any way to do a health check by Route53 ? Can I set a IAM policy that certificate rest API on Route 53 orcan the health check call include credentials?