There are two possible problems:
Firstly, simply plugging in the headset is likely to disconnect the speakers. (Whether it does or not will depend upon the way that your PC is wired. Try playing an audio CD to see whether the sound comes out of just the headset or out of the speakers as well).
Secondly, the reason that Skype users normally use headsets, rather than just using a microphone while the sound comes out of the speakers, is that the sound going into the microphone might be fed out of the speakers (and then back into the microphone and out of the speakers . . . etc, etc). That creates 'feedback', which is the awful howling sound that you hear when a stage performer has got the microphone too close to the speaker system.
Go to your nearest Maplin store and ask them for a headphone splitter. (You plug it into the headphone socket on your PC but it has two sockets on the other end of it). Then go to a 'pound shop' and buy a cheap earpiece, so that you can plug your headset into one socket and the earpiece into the other.
Chris