I don't know if you have a clear idea of what you want or an existing tool. If so you can ignore most of below!
Wearing my woodworking hat the term ''scratch stock'' conveys the idea of a cabinet scraper with a particular profile (which might be quite complex), also the blade would probably be sandwiched between two pieces of timber to provide a grip/handle and some sort of guide/fence.
The blade will cut because, like a cabinet scraper, it has a turned over (hooked)edge mad by burnishing a sharpened edge.
For the blade I would think 1 mm adequate and some sort of carbon steel. Short of buying something (horror horror) an old woodworking panel saw would provide a life time source. An ordinary resharpenable saw is probably easier to cut and shape than a hard point, Blunt saws at a car boot ought to be cheap enough to try both. A dremel or clone with cutting wheels/pioints would be my choice to cut and shape. The resharpenable saw may be best if you go down the soften-shape-harden-temper route.
John