A CD PLAYER whose sound quality NOT AFFECTED by the DAC?

Why even use a separate streamer? Get, like I did, a Sony Universal WiFi player and access streaming services via a smartphone. I then added a DAC, even though the Sony's DAC sounds excellent!

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Don't be silly.

Digital sound cannot be heard without a DAC unless you have digital ears.

But OP is correct in implying that DACs are the Achilles Heel (or is that Hell?) for all digital sound.  Clock error and dither can never be eliminated.

I am not familiar with the CD player the OP has but it sounds like a multiple disc player.  Such players were made for convenience in the pre streaming days and usually the DAC in the player isn’t very good, so it’s possible the Node 2 DAC is better.  The latest Node DAC is an improvement over previous models and we are not sure which one the OP has

.  In addition the OP seems to lack a conventional pre amp.  Some DACs have enough gain that for digital sources they don’t require a pre amp.  However I have always preferred to use a pre amp because inimo they sound better, but ymmv.  My advice would be to use the integrated amp in the closet; trying running the CD player directly into the amp, and then compare the sound to the CDP running into the Node which is the connected by analog to the amp.

Get a CD transport and be done...then you can buy a dac to suit your taste. 

As just said by @mahler123, there were very few Multi Disk Players that sounded any better than a portable player. CAL and Rotel had decent ones but any mass market unit is compromised for convenience.

I am very happy with my Rotel 1572 CDP (Balanced into my Lux) that replaced a 1072 which both easily bettered my 2 OPPO 93s