I’d suggest asking Ayre, as I suspect the most significant factor that would be involved is how the balanced and unbalanced output circuits of the CDP are implemented. But FWIW my guess is that changing to an XLR-to-RCA cable is unlikely to provide any benefit.
If you do go with an XLR-to-RCA cable, however, MAKE SURE that it does not ground either of the two signals in the balanced signal pair. My impression is that most such cables, and also most XLR-to-RCA adapters, connect pin 3 (which carries a signal) to pin 1 (ground). That would be appropriate when adapting an RCA output to an XLR input, but can cause problems or conceivably even damage in many cases when adapting an XLR output to an RCA input. This thread, which also involved a solid state CDP, being an example.
Good luck with the new preamp! Regards,
-- Al