Why is there any question? The 9600 was discontinued well before OS 8.6 came out so obviously there won't be a machine-specific installer for it (those are only for new machines) and a machine-specific installer for another machine won't want to run on it. So clearly you need the retail disk.
As to the first part, machine-specific install CDs exist for three reasons:
#1: For brand-new machines released between official OS updates the build of the OS on the CD, while claiming to have the same version number as the current retail version of the OS, might have some machine-specific drivers or other support added to it that's necessary to support the new hardware, essentially making the OS on it a "pre-release" version.
#2: The machine-check is just there to prevent someone from using the disk included with a new computer to upgrade all his old computers; the OS on the CD may be completely bog-standard otherwise, the check is just in the installer.
#3: The "install" CD is actually a "recovery" CD that installs additional programs not included with retail versions of the OS and the machine check is likewise there to prevent someone from getting this software for free on computers not "entitled" to it.
Honestly I'm sure wherever you end up getting 7.6.1 it's going to be pretty much the same, but since the 9600 did technically debut in-between 7.6.0 and 7.6.1 it's *possible* the version off its restore CD has some special tweaks missing from the retail box version of the OS, so... go with that?
(Truth be told, of course, the machine will almost certainly work far better under 8.1 or later, as every version of System 7 suffers from most of the OS running in emulation. But I'll grant there might be historical value to having a 7.x install around.)