After doing some research, I found some stuff that may interest you...
http://www.macmod.com/forums/viewtopic.php?t=1381
According to this link (
http://support.apple.com/specs/powermac/PowerMac_G4Cube.html) I found this-
Digital amplifier and speakers with Harman Kardon audio technology
—Total power output: 20W
—Frequency response: 80 Hz to 20 kHz
—Single USB cable carries both power and audio; plugs into USB port on the G4 Cube or a display with ADC
—Removable covers protect speaker cones
—Digital amplifier module includes locking loop for theft prevention and minijack for connecting stereo headphones
And another link, selling them for nearly $300-
http://www.welovemacs.com/m7963.html
All of that being said, I wouldn't be too hasty to hack them apart.
Now one thing is for sure: the G4 cube had a more powerful USB bus. I am not sure how it works, I have looked around and can't find a voltage or amperage rating for the cube's USB. All we have a is wattage number, which doesn't help. The typical USB port can push out about 5 watts while the cube's bus could do about 20 (10 to each speaker). I'm not sure if the voltage required is still 5V (USB ports are 5V) but with a higher amperage rating or what.
Now I am sure of a couple things:
It is possible to get them to work with your machine without hacking them at all. First of all, they technically still work when plugged in, just at a really low volume (due to the lack of power supplied from the USB port). Apparently, the USB busses on most ADC monitors are similar to that of the Cube's. If you have an ADC monitor, just plug the speakers into its USB port.
Your other options before hacking the speakers are to either purchase an ADC capable monitor (with appropriate video card if you don't have one), or just sell them on ebay and use the money you make to get some speakers that actually work.
Now... you basically have two options when it comes to hacking. Theoretically, both are plausible. I wouldn't try them if you are a novice with electronics. You will need a good soldering station, flux, and a steady hand.
First, you can perform the hack that you suggested - cut the speakers from the amplifier and hook them up directly to the computer's internal amplifier. I'm not sure what the internal amplifier is rated at in wattage (its definitely not more than 20 W), but I don't think this is the best option. The speakers would surely be underpowered, and you'd be driving two speakers with a low powered amplifier which was meant to power one single internal speaker. Most internal speakers are rated at something rediculously low, like 2-5 Watts. All this to say, I doubt your sound would be much better with the cube speakers from the original internal speaker, because you are using the same amplifier. Ultimately, the amplifier is what will make the difference.
The second option is to hack the cube speaker's amp entirely. The USB connection passes audio and power, that's all. This means it is theoretically possible to open up the amp, separate the power from the audio, and make indivual connections for both. You would need some electrical training and experience. I could do it but I don't have the speakers to reference to guide you. If you were somehow able to separate the power input, and hook up an external power supply (say, a 5V adapter), and create a line level input for audio (typical 3.5 mm/1/8" input), you could power it from the wall and get sound from the headphone jack.
I don't know if that is too involved for you. Let me know if you are interested in this mod, I may be able to help you further...