Start with a desired thickness thin until it survives the bend radius.
Bent lamination thickness.
For very small shaker boxes in cherry even 1 16 can be too thick even after steaming.
How thin you cut the strips depends on a number of factors include the wood s natural bending properties the severity of the curve and your tolerance for springback.
There s some info in the may issue of american woodworker on bent wood laminations.
Bending plywood is available in 5 16 and thicknesses and comes in several species including poplar birch and lauan in standard sized sheets 4 x 8 with the veneer layers running either lengthwise or widthwise.
Shallow curves can be made up of fewer thicker laminations while tighter curves need more thin laminations.
Bottom line do as previously suggested.
It s messy but rewarding to see a gracefully bent piece of wood emerge from a glue encrusted form.
Once the parts are formed changing the overall thickness will be very difficult so take the time to figure out the number and thickness of strips needed to make up your part.
Cutting laminates on the bandsaw cutting your own laminates is best done with a bandsaw.
The thickness of the parts is largely determined by your bend.
As to ply thickness.
The process starts with ripping some thin strips of wood and applying glue to each strip.
For a 6 radius bend using kiln dried walnut the best i could do was 13 laminations per inch.
Lamination ply radius thickness 2 4 3 32 4 8 1 8 8 12 3 16 12 1 4.