Can I change the socket of a light fixture by simply cutting the old one off and re-wiring?
It looks like the Hue system doesn't have any candelabra sized bulbs.  I don't see a Hue switch that would let you control the fixture as is.  All the Hue system bulbs look large.  

There are adapters that will let you use standard bulbs in an e14 socket:  



I'm just not sure the bulb will fit in the fixture with the adapter - looks like it may be too small even without the adapter.  It might turn out to be easier to change the fixture.  

(BTW, if you are in the US, you may want to check that it's really E14 and not E17 intermediate size socket.)