While a DSN-less connection allows your to connect without a DSN, you would still need a Database Name. Pervasive Database Names can be created on the fly using DTI or DTO. Using C#, I would suggest DTO.
If you can't create a Database Name, you can use OLEDB. It supports using a path in the Data Source
parameter of the connection string as documented in the Remote Connections section of the OLEDB documentation.
One more caveat, make sure to compile your .NET program as x86 and not AnyCPU. The Pervasive OLEDB provider is only 32 bit. If you install your app on a 64 bit Operating System compiled as AnyCPU, it will look for a 64 bit provider and fail.