Suppose after using the facilities there is no water available, should one say Asher Yatzar without washing their hands?
Yes, one should say Asher Yatzar even if he did not wash his hands. And if one was mishafshef, meaning he wiped the sprinkles of urine, he is required to clean his hands, even still, when there is no water he can wipe them on any surface that will clean them. Shulchan Aruch siman 7 siff 2 with Mishna Berurah s.k. 5.