There are polymer clay blades and tissue blades. For the thinnest slices, you need the thinnest blade you can get, so a tissue blade. (These are medical lab tools, not meant for polymer clay, but we use them all the time anyhow.)
The stiffer more commonly found polymer clayblades can also be used, but likely your slices will be thicker.
You can let the cane firm up before slicing, roll the cane into the blade while slicing, or just reshape the slice after cutting. This is polymer clay, not high precision machinery!