With those blade dimensions, 3/16" tops, probably.
Perhaps think more like a "heavy duty" machete with 1/8" stock, depending on what grind you're going with.
So, depending on grind, I'd say between 1/8" and 3/16".
Although you could make it manageable with 1/4" if you do a full height flat grind...but I'd probably go with 3/16" myself.