I would imagine a wet stone or an oil stone.....you may even be able to do it with a file or a grinder.

You can replacement blades for Felcos...not sure about other makes

Try a butchers steel. But I don't think that they need to be super sharp as they use more of a shearing action like scissors do to cut.

I use a small oil stone on my Felco's - remember to keep them clean too as sap and dirt on the blades don't allow them to work properly.