Especially if the hatband is made of suede or another delicate, water-sensitive material, you may be hesitant to steam or use moisture to reshape the felt.
In this case, if the wrinkles primarily affect the crown, you can:
1. From the inside, push out any dents and wrinkles, using your hand or a hat brush.
2. Use cloth or a towel to stuff the entire crown area, or place it on a wig stand, if it's available.
3. Leave the hat in this position for multiple days.
4. After some time, remove the filling from the crown and see if the hat retains this shape. Going forward, be sure to store your hat in this manner or inside a hat box.