Depending on the brand and sensitivity of the CD player to mechanical vibration, it may not affect your CD playback at all. There's a lot of audio voodoo and nonsense perpetrated about mechanical vibration affecting sound quality with solid-state components. Normally, there is no effect whatsoever.
But there is a mechanical aspect to CD playback. The optical pickup is usually on a mechanical sled that is servo-driven across the radius of the disc, so it can be knocked off-course by fairly blunt jarring. Minor vibration doesn't usually cause any effect.
There are two types of vibration generated by your subwoofer-- mechanical, transmitted through the subwoofer's feet to the floor, and then through the floor to the CD player. If the floor is concrete, or wood parquet over concrete, that is unlikely to occur. It will happen with older, springy wooden floors.
Then there's acoustic energy generated by the sub's acoustic output and standing waves in the room. Insulating the sub's mechanical vibrations won't do anything to damp the acoustic energy and resonances that may result..
You can use compliant pads of rubber or old squishy tennis balls under the feet of the sub to isolate mechanical vibrations. Most CD players are quite resistant to acoustically born vibration, so try it out first.
Acoustic and mechanical vibration really only become a serious issue with turntables and tube gear, where the tubes often become microphonic and susceptible to acoustic and mechanical feedback--yet another liability of tube equipment. The plastic dust covers on many turntables used to function as a primitive microphone feeding acoustical energy to the turntable base, tonearm, and cartridge, especially at high volume levels.
Axiom Resident Expert