This should be the way to go here - https://github.com/aws-samples/sagemaker-run-notebook. In essence, one uses a lambda function to trigger an AWS SageMaker Processing Job. This is kind of like running a notebook on an AWS SageMaker Notebook instance without having to think about provisioning the instance and killing it after finishing the job.

It uses papermill to run the notebook on a sagemaker instance. Users can pass a custom docker image with their own custom kernels.