You won't have to install Ingres/NET on the Sun machine. The ODBC drivers you would install on your HP server would open Ingres up to ODBC clients, i.e. make it ODBC compliant. Microsoft Excel, for example, can access ODBC compliant databases. Your Sun server also has ODBC client software, which would talk directly to your HP's ODBC driver which would be configured to interface with Ingres.
I did this very thing years ago on an HP 9000 running Ingres 6.4/06 on UX 9.01. I got working, albeit with quirks, and managed to read data right out of Ingres into Excel.