Can you wire a US CD player to a UK plug?

It might be possible but check the following things first:

On the rear of the player is an information panel that will state the power supply requirements. If it does not include 230V AC as an acceptable power supply, then it's not going to work.

Next, check the mains lead. Does it look like a figure 8? If so, it is not a double insulated lead and therefore is not approved for use in the UK. UK mains wiring demands a second insulator because of the higher voltage used for mains power and therefore the higher risk of making contact with it.

If you can confirm that both of these points are in order, there should be no reason why the player won't work in the UK.