Think if you're very careful you could steam it briefly in front of a kettle then shape it - if you hold the brim and gently wave it up and down you should get a good shape - have done this with stetson type hats and had great results but never with straw so be careful!
Mags 22 you will find you'll get more help on here if you take the trouble to thank those who took the time to answer your query -it is, after all, only polite to do so.