Merging 4 X CD Sources through one DAC

I have 4 X Sony CDP-CX555ES CD players (1200 CD capacity) controlled by a Nirvis Slink-E that I need to feed into a single input on my Audio Alchemy DTI Pro 32 / DDE 3.0 DAC system.

I have looked into "Auto Switchers" that accept 4 TOSLink or coax inputs that activly seek a signal and automatically switch to the active channel - such as the Inday DA4X-R and the Audio Authority 1177.

My concerns are that these switchers will introduce signal loss / artifacts and also defeat the cross fade capability of the Sony CD players. Does anyone have experience and advice in this area?