How can I create an ad-hoc domain user on SQL Server
You cannot actually login to SQL Server with any domain account. You can either pass a SQL Login with its password, or you can logon using "Windows Authentication". What the latter means is that the account that is executing the windows executable is passed to SQL Server to authenticate. 

That means you just need to execute the app using a local machine account and add that account as a windows login to SQL Server.



If the application on the other hand is running on a domain computer and you just pointed it to use SQL Server on your machine, you are out of luck. However, if you were able to change the connection string to point to your machine, you should be able to just add a SQL Login to that same connection string.