Obviously it's hard to know what's best without seeing the actual gear, and we've no idea of signal levels or impedances!.
As 'baftab' looks to have very little experience?, I think the 'one channel' solution is probably the best for him.
So I should try unplugging one of the speakers, and feeding the output from your CD into your circuit - this should work fine, but you will only hear one channel from your CD, and see the display from the other channel.
Once that's working you could try connecting your second speaker as well, due to the relative impedances you should be fine connecting both your circuit and the speaker in parallel to the output of your CD.
I won't worry about only one side feeding the display!.