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.
There is a possibility that you can obtain an Ingres 6.4 ODBC driver for your HP server from OpenLink Software and you won't need an Ingres/Net installation either. Please contact email@example.com and if this still exists, you can obtain it there. or will be pointed in the right direction.
I'm sure your friendly CA account manager would love to sell you some middle tier to talk your java (OpenRoad app server perhaps), although you may have to upgrade Ingres to get any of them to work.
CA stopped supporting 6.4 a few years ago, and I suspect that you will get a lot further if you consider upgrading Ingres - 6.4 to II 2.? can be painful, but CA have a lot of literature on their support web site which may help.