CDP directly into amp?

Yes you can. Ideally your CD player will have a quality volume control, high output, and low out put impedance. Your interconnect should be short and have low capacitance. The McCormack amps are particularly good choice due to their rather high (for solid state) input impedance and IMHO it's punchy extended sonic signature. Choose a McCormack that is on the sensitive side. The cons include a varying impedance depending upon volume setting and the chance of diminished dynamics.

Of course if you have a CD player that you like and wish to keep, an alternative would be to consider an amplifier with an attenuator on board - or an integrated amp. But the advantage of an amp with an attenuator is that it will typically sound better than a comparable integrated amp (at least that is what I have observed in my own listening tests) The only problem is that sometimes amps with attenuators lack remote control functionality.

Otherwise both Phild and Unsound have offered the exact same advice I would throw your way in terms of cables, and considerations for variable out CD players. And yes McCormack would be a great amp to consider if you plan to use a CDP with a variable output stage. There are other good choices as well but if you like the sound of a McCormack, it has the right electrical characteristics to work in such a configuration.

How much do you want to spend? Most CDP's that are remotely good at regulating analogue volume are pretty pricey.

KF

The least expensive solution would be to pick up a used Marantz CD63SE or better yet the CD67SE with remote. The remote has a volume control, and the player is certainly of high enough output to do exactly what you are looking to do. These are excellent players, esp for that kind of $. Used should set you back no more than $200-$250, and that for a player in excellent shape. New MSRP was $500, often discounted ca $425. There are probably other units w/volume controls, but not usually on the remote feature. Finally, with the Marantz players, they power up to full volume, so you will want to leave the player on all the time unless you will remember to lower the output before playing music. HTHelps.

How handy are you with a soldering iron? I recently direct wired a very good quality stepped attenuator into my CD player. I mounted it inside the chasis with a long shaft to a volume control knob on the face plate. It is directly fed into a CJ amp. Works very well and I am very satisfied.

The cons can be mismatched impedances, which you can prevent and elimination of future flexibilty in your system. But this process is reversible should you want to go back to a preamp.