On Windows you can only run Greengrass in Docker container.
But if the only thing you need is MQTT message exchange between your app and AWS IoT Core, you don't need Greengrass at all. I'd even say Greengreass would complicate things more.
Instead write MQTT client extension for your app and it will publish and subscribe directly to AWS IoT Core.
Here you have sample .Net MQTT publisher/subscriber application:
https://github.com/aws-samples/iot-dotnet-publisher-consumer
If you want to built in more functionality here is .NET SDK API reference:
https://docs.aws.amazon.com/sdkfornet/v3/apidocs/Index.html
Happy coding!