I usually do most of my payments with a wire transfer. I can do an international wire transfer online with my bank or credit union and it costs me $30 per transaction. Usually a wire transfer for the down payment when you book the hunt, another wire transfer to make the final payment 60 days before the hunt (if required). The last day of the hunt, when the trophy fees and misc are totaled up, make another wire transfer before you leave. It usually takes 3-4 business days for the transfer to clear. Only one time did a PH not agree to this, so I pre-paid some estimated trophy fees. The PH actually owed me a little money at the end of the week.
I also travel with some cash for tips for the trackers, camp staff, etc. US dollars are gladly accepted everywhere. Just as a FYI..........if you are bringing a bunch of US $100 bills, get the new ones. Some places won't accept the older bills.