HP LaserJet 1005 is connected to Windows 7 (x86) workstation and we cannot change that (it needs to be Windows 7 and needs to be connected there). Windows XP 32 bits drivers are used because HP does not support Windows 7 x86_64 with this printer. Printer is shared across a local network (SMB), but only users with 32 bits systems can use that printer (driver issue).
The idea was to delegate one Linux workstation to work as a proxy between all 64 bits Windows systems and that one particular Windows workstation where printer is connected. Is it possible at all? How to achieve that?
This is not scalable. The HP LaserJet 1005 is very much past the end-of-life stage. As a printer, you can see that its support is extremely-limited. If you can't even support the very clients who need access to the printer, the printer is the problem!!
My best advice is to obtain a printer that supports your clients. If you're going that far, you may as well ensure that it works with Linux, too... (RAW or CUPS-style printing). I manage a lot of production printing environments, and tend to check against the Linux Foundation printer database before making purchasing decisions. Also, make sure the device has an internal print server (networking), so that being connected to a workstation isn't a dependency.