Bottom line do as previously suggested.
Bent lamination thickness.
There s some info in the may issue of american woodworker on bent wood laminations.
The thickness of the parts is largely determined by your bend.
For very small shaker boxes in cherry even 1 16 can be too thick even after steaming.
Start with a desired thickness thin until it survives the bend radius.
As to ply thickness.
For a 6 radius bend using kiln dried walnut the best i could do was 13 laminations per inch.
The process starts with ripping some thin strips of wood and applying glue to each strip.
Bent lamination is a process of bending thin strips of wood using lots of glue and lots of clamps.
Anything thicker was prone to splitting.
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.
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.
It s messy but rewarding to see a gracefully bent piece of wood emerge from a glue encrusted form.
Shallow curves can be made up of fewer thicker laminations while tighter curves need more thin laminations.
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.