Quite a few of the internet cafes will send a fax for you, or scan and email.
I think the last one I used was on that road in the centre of town that has the Euro guest house and Tanawit hotel on it.
May be over complicating things, but if you have PC and internet connection (and can scan documents) - another possibility is to send using something like "Pam Fax". Free software add-on to SKYPE.
"Hope is a good thing, maybe the best of things" - Yma o Hyd.