There were/are a number of ways to sharpen microtomes Wullie, depending on the type. The one shown above with a long sleeve and no handle is often referred to as a 'microtome knife' and if it is not sharpened in the sleeve a similar sort of adjustable sleeve is provided. These fir into machines and are not really used in the hand. They come in many cross sections - some are sharpened on just one side, others on both sides. Here is one on a round lapping plate:
Attachment 158100
And below is a home-made jig that sharpens (usually) just one side of the blade. Commercial models were also made:
Attachment 158101
Lastly we have a microtome razor, which looks like a straight, but users tend to call it a sectioning razor - this is only sharpened on one side as you can tell from the specimen holder - the specimen is embedded in paraffin wax and the razor drawn over it. Sharpening both sides would elevate the cutting edge and give a sample thicker than wanted:
Attachment 158102
The above are still available. Lord knows where they are made, though!
Regards,
Neil