How and is it possible to use a local file for a CloudFormation stack besides an S3 bucket?
I'm afraid you can't. The nested stack files must be in S3 as far as I know. You have a couple of options:
Have some automation in place (e.g. aws-cli + shell script, or better ansible) that when executed will upload all the templates to a designated S3 bucket and then execute the the CloudFormation deployment.
Use some templating engine like Ansible + Jinja or similar that can build a big CFN template from little snippets saved in separate files. With Jinja you can also use loops, lookup variables, etc, to build your final template file. Then again you can use the same Ansible playbook to deploy it. Or do it manually as it will only be a single file.
Hope that helps :)