If you are strongly a cash-only type person, I guess you could have a spouse, relative, good friend, etc. send money to you every two to three weeks. Walmart, Western Union, MoneyGram, and others offer cash transfer services but the fees I think start at $6 & up and you may only be able to send a few hundred dollars. I am not overly familiar with them but have seen them even in smaller towns, i.e. I think Western Union can be sent to Dollar Generals which are in a lot of rural locations.
Like others, I use a combination of cash ($100-$300 always on hand with always some small denominations), debit cards (Schwab Bank does not charge ATM fees for anywhere in the world and will reimburse you if you are charged, regardless of amount or location), and credit cards. I also scatter cash in various places on my bike, i.e. wallet, handlebar bag, panniers, drop tube, etc. in case I lose my wallet or my bike is stolen, I hopefully have a few places with cash left over.
Have a great trip!