I'm not sure I see the problem. Or there isn't a problem. This appears to be a road double with shimano or shimano compatible drivetrain. Sheldon Brown says the front chainline measurement should be 43.5 mm. That is the distance from the centerline of the seat tube to a point midway between the two chainrings. If someone has used a bottom bracket with the incorrect spindle length this measurement could be off. However, you stated that the problem was not there with the old cassette. If I understand your description correctly I doubt that the new cassette is installed incorrectly. There's not enough room for a spacer and a spacer would cause a chainline change in the opposite direction. On a normal 9 speed hub body the cassette can't be installed any deeper to cause your problem. This assumes it's an 8/9 speed cassette body. Incorrect axle spacer installation could move the wheel to one side and thus move the cassette position. Has any work been done on the wheel? You realize that on a double crank with a 9 speed cassette the chainline is never perfectly straight? Do you see more deflection in the small chainring and large cassette cog versus the big chainring and smallest cassette cog? They should look about the same.
It is true that if you tend to ride a lot in the outer or inner cassette cogs with more deflection the chain will theoretically wear out faster but I'm not sure by what percentage. If you are worried you may want to reconsider your choice of cassette and chainrings. You will get the most chain life if you do most of your riding in the middle cogs of the cassette. But personally, I wouldn't worry. Chains are relatively cheap components compared to cassettes and derailleurs.