This idea should work, at least partly. But it will certainly need the general humidity of the hat increased. If it is dried out, like I suspect it is, it will retain this shape indefinitely. But adding moisture can be perilous to the piece if the moisture is then not removed. It needs to be a three part process. 1) Slowly add humidity to the hat, one method is to have it several times in the bathroom where you take hot steamy showers. 2) Gently form the hat back to the correct shape and stuff with clean rags to hold that shape. 3) the most important of all is that you must actively REMOVE the humidity from the hat. Don't let it just sit and dry out. Otherwise you just activated every mold spore in the felt and threads and gave it the precious water they need to flourish. The hat will become a mess in weeks. Put it in a small room next to a dehumidifier. 50% is a low setting, but go for lower, like 40. IMO, Don't do step 1, if you can't do step 3. Good luck!