This article is from the Recreational Figure Skating FAQ, by Karen Bryden with numerous contributions by others.
Although opinions vary, the consensus is that hand-held sharpeners
cannot replace a good machine sharpening. You cannot change the hollow
radius easily and you should not use them on tapered blades. Having
said that, they can be very useful to maintain a sharp edge or get rid
of small nicks, particularly if you don't get the chance to get a
proper sharpening as often as you would want because of lack of
reliable competent sharpeners in your area.