i've actually done this twice before for my gf and for my bro in law... Ejets...
firstlty i used two long sewing needles... top and bottom and wiggeled the snapped bit out... easy yes...
bear in mind this was just a third of the length, not to much snapped off...
BUT for my gf's on she had snapped like half the key so i had to take the barrel out... jiggled it and tapped the bit out... more fiddly if this is the case...
getting the barrel out aint that bad... its all the stuff you have to take offf to get to the barrell thats a ball ache...
maybe be worth driving round to locksmiths as they know best...
good luck