OK, so realistically the only thing you can do is remove the case from an existing CD player, and perhaps even remove the innards and lay them out. But all the electrical connections would need to remain the same, and you won't be able to make any electronic modifications if you want it to actually work. Also, see the stuff about electrical safety below.
Forget making your own electronics - it's not a trivial job to play a CD, so I doubt you'll have the time or expertise to do that.
You will also need an amplifier. There are countless designs online, and it's possible you will have time to build one, especially if you buy a kit. If not, you'll have to open up an old one, like the CD player.
There are potential electrical safety issues with dismantling electrical products, although virtually all the commercial products I've worked on are safe even with the lid off. Even so, if you want to remove the innards completely from a CD player or amplifier you will need to think about electrical safety and earthing. If you are still at school or college, there might be a qualified member of staff who can advise you and check its safety.
To be risk-free you should really stick with battery-powered products. And that means you have a problem: the most "interesting" and "cool"-looking CD player mechanisms are the old ones which people would use in their hi-fi systems, and unfortunately they are all mains-powered. Battery-powered CD players are usually (always?) portable, which means everything inside is tiny and, basically, not very impressive-looking.
Depending on your time, skills and budget you might be able to convert the player and amplifier to battery operation, but this is likely to be quite a big job.
In summary:
1/ Your idea is impractical, and shouldn't even be tackled if you are using mains-powered devices.
2/ There's no chance at all that a girl will be impressed by a gutted CD player and amp laid out on a wooden board, even if it is playing her favourite track. "Nerdiness" isn't on most girls' list of attractive traits in a guy.