Hi Robert,
Confused by your question or maybe I am misreading what you are saying?
Your ASP.NET Web services do not need to be migrated to .NET Core... PowerBuilder's HTTPClient/RESTClient can call any REST Web API no matter what underlying technology the Web service uses. It doesn't even have to be .NET... you can call Java, Python, etc.
Now as far as if you want to create a new .NET web service using PowerBuilder's .NET DataStore object or use our automated C# migration solution to move some of your PowerScript business logic to C# Web APIs, then for those new Web services you create using .NET DataStore you will need to deploy that with .NET Core.
But even if you are doing new .NET Web services with .NET Core, you can still keep your old .NET Web services like they are and integrate them all into your project. That's the beauty of the REST standard.
Regards,
Armeen