If you want actual "shaving sharp" then you want the type of steel used for razor blades. That would be a steel without carbides. 13C26 taken to a high hardness would be the thing. Such an alloy will retain it's shaving edge longer, but would then dull much faster than a carbide-containing alloy.
Steels with carbides are like concrete, got chunks of rock in it.
Steels without carbides are like cement, just fine particles.
When you start cutting with a carbide containing alloy, the carbides (bits of ceramic) begin to protrude from the surface as the steel is worn away around it. That means you lose your "shaving edge" relatively quickly. But once exposed, the carbides wear MUCH longer than steel. That means that the somewhat lesser edge is retained much longer.
Steels without carbides do not have chunks. So, the fine edge lasts longer. But then there are no hard particles to resist wear and the edge degrades faster.