I have not upgraded my CD player yet, so I do not speak from personal experience, but judging from the spec sheets and the outstanding performance of the AD8610 in other applications such as a headphone amp I am building, it is probably a great choice for the I/V converter, filter, and line out of the CD player.
I have a Denon DCD-1420 which uses various Japanese opamps such as the 2068, 4556, and 4570. I'm not sure how much of an improvement the opamp swap will achieve, but it will be interesting to see. I'm not expecting miracles, but more sweetness and less grain would be nice.
The circuit board for the CD player headphone out section is upside down, inaccessible from the main compartment, and requires major disassembly to get a look at. I might be tempted to use an opamp with higher output current for the headphone out if the opamp drives the headphones directly, but if the opamp is buffered then the AD8610 is probably the best choice again.
There are many good opamps to choose from, get a variety if you can, and compare them. The differences become subtle at a high level of performance. I'm in the process of comparing several opamps for use in headphone amplifiers and CD players, including the AD8610, AD825, AD8512, AD823, AD826, OPA2132, and a few others. I've also been working on a custom audio test tone CD to help evaluate the opamps and the CD player. So much to do.
