Welcome -
There are two styles of carbide cutting ends commonly used with pens.
Cup style cutters -- Hunter Hercules, and the Eliminator are two that come in smaller sizes nice for pen turning. These use a very fine grain carbide and can be used in scrape, bevel following, and shear scraping cutting modes.
Flat scrapers -- There are several of these on the market, and a couple of them are noted above. The EZ line has not been mentioned. These tend to be uses as scrapers, but can be used to shear scrape (very fine whispy spiral shavings). I personally like the PenPro but also have some of the EZ line.
If you make your own, please be sure to get the mounting screw with the insert. Carbides, especially the fine grained ones are brittle and need the tight support of the mounting screw as a firm fit to the recess in the cutter. The recess an screws are not standard across the board.
Plan on using a fresh edge for fine finish cuts regardless of which brand you use. The finish work diserves a nice fresh edge -- and after it is used for finish cuts for a while, you can move it over to roughing and use a new edge for finish work. Sandord or similar markers will let you mark the edges for use. I use very old edges for hogging wood, and especially bark or dirty wood.