Ugh... this sounds like an extremely complicated solution to maintaining an impractical situation.
First, if you must rely on the IR codes built-in to the Sony device, chances are EXTREMELY slim that the ones needed by the volume control you're considering would be anywhere in its database. Remote IR codes aren't like just finding the right shape plug to connect two items - it's more like trying to guess the combination to a 12-digit padlock.
Second, what is the amplifier you're talking about? Are you sure it doesn't have some alternate control input? Many old amps have wired IR inputs on the back. And how is the IR broken? Perhaps it would be simpler to repair that.
Third, I wouldn't doubt that such an inexpensive/unknown analog volume control might degrade the sound on what you're controlling, thus nullifying the reason to work around a good amp in the first place.
Finally, assuming funds are tight, have you considered getting an inexpensive (ie. refurbished / old model year) receiver with preouts and - if you're so set on the sound quality from your current amplifer - merely using it as a remote control switcher/preamp? If you get one with digital inputs, you likely wouldn't need the separate D/A converter.