The way to re-sharpen scalpel blades is to rub the BACK of the blade tip on the sharpening stone reducing the blade length slightly. This changes the blade shape slightly from its triangle shape . This way you do not sharpen the factory sharpened part but merely reduce the blade length until a new tip is formed further down the blade. The small diamond whetstones are quite cheap in very small sizes now and could be used for this.
The Retractaway scalpel blade holder from Swann Morton is by far the safest scalpel. The blades are the normal No 11 or 10A etc and are held just as firmly as the simple holders. Well worth the slight extra cost.

If you wish to obtain suitable fine abrasive powder to use on a leather strop then a handy substitute is a the white liquid type slightly abrasive bathroom cleaner ( such as Cif in England ) Allow some of the liquid to dry out to a fine powder and mix with oil and apply to the leather. I suppose you could use the liquid itself but it would rust your tools. A leather strop used with this very fine abrasive powder is the best way to put a fine edge on carpenters tools such as chisels, planes etc but its probably not worth honing scalpel blades if they are available cheaply.