You don't need to cut the old one out, unless its really old and hard, just flick it out with a pick or small screw driver etc. you also don't need to remove the gear to refit, a new one will be stretchy enough to roll over it.
Last time I bought one I just took the dizzy to my local "nuts and bolts" and bought 2 different sized ones that were close enough. One was slightly too fat and the other fit perfect. From memory it was about 50 cents for both! ;)