My speciality, assuming you have a router table. I'll assume you have a way of resawing the stock into narrow strips and are concerned about producing a smooth face. A band saw is my preference for the resawing but a well set-up table saw will do.

The trick with the router table is to use a fine carbide die-grinding bit in place of a standard router bit. Trap the stock between the bit and the fence and use "fingers" to hold the stock securely against the fence as well as keeping your fingers out of the bit (right image). I've made purfling for guitars paper-thin with this technique. You may have to search on-line for a quality bit. Preferably work with closed and tight grain woods. Although the rosewood in the images was anything but.

You can't remove a lot of material with this technique. It may take multiple passes if your resawing was fat. Be sure the bit is square to the table and parallel to the fence.

You may note the stock here is laminated, maple on top, rosewood on the bottom. The stock to form this was also made in the manner described above.

EDIT: Oops, appologies. I didn't note the "hand tools" in your title. If you've got a lot of this to do, a router table is the way to go (unless you have a drumb sander).

By hand, maybe try a cabinet scraper. Cut two wooden triangles from 1" stock. A base-to-height ratio of 4.5":6" gives a 60° angle. Cut out some of the interior so you can clamp the scraper to the angled faces. Use stock that is overly long so you can clamp the ends to your work table. Your table supports the bottom of the stock and probides a surface to run your scraper-jig over. The height at which you clamp the scraper ultimately gauges the thickness. Sharpening and burnishing a cabinet scraper is an art.

By router: I'll assume you have a way of resawing the stock into narrow strips and are concerned about producing a smooth face. A band saw is my preference for the resawing but a well set-up table saw will do.

The trick with the router table is to use a fine carbide die-grinding bit in place of a standard router bit. Trap the stock between the bit and the fence and use "fingers" to hold the stock securely against the fence as well as keeping your fingers out of the bit (right image). I've made purfling for guitars paper-thin with this technique. You may have to search on-line for a quality bit. Preferably work with closed and tight grain woods. Although the rosewood in the images was anything but.

You can't remove a lot of material with this technique. It may take multiple passes if your resawing was fat. Be sure the bit is square to the table and parallel to the fence.

You may note the stock here is laminated, maple on top, rosewood on the bottom. The stock to form this was also made in the manner described above.