I usually like to use some Stretch Velvet Ribbon in my hats as it makes them super comfortable and it also helps to make the crown of the hat smaller! You can get that at www.houseofadorn.com. They also sell foam and felt hat band tape which can also be used to reduce the size. I hope that helps!
It would depend on the types of materials you use to make a hat. I do not work with sinamay so I am not sure on that but with felt there are several options. The stretch velvet or stretch grosgrain might be an option. I usually either use foam or felt under the grosgrain band and/or wet the grosgrain band and if possible the felt. Place the hat on a smaller block and steam. Let dry overnight and the felt and band will usually shrink to the size of the new block if you do not need a huge amount of shrinkage. Once it has shrunk then you can add the felt or foam under the grosgrain band for any additional amount of shrinkage you need. Fabric hats on a buckram base use a similar method.