How might one fly from KRYN to SDRS in a de Hallivand DHC-6 Twin Otter? First of all, this is not a flight I'm attempting myself; it's for a writing project. I myself have absolutely no knowledge at all of flight. The plane would depart from Ryan Airfield, Arizona (ICAO: KRYN) and land at Resende Airfield (SDRS). As the de Havilland DHC-6 has a range of only 886.7 miles, I assume a great deal of refueling is required. I have no knowledge of flight, so the logistics of a flight this length, (about 5,900 miles), in a light aircraft, are completely alien to me. Importantly, the passengers on the flight (4) do not have passports, but must still be able to enter the country. I’m guessing this means they’d land at a small airport/airfield. Assume the pilot has connections that allow his passengers to bypass any security at the small/private airport. The most important information would be: how long it would take, where/when they’d need to stop on the way, and where could the final destination be. 

Your help is greatly, greatly appreciated! :)

Also, assume the situation is urgent and the pilot is a risk taker. He wants to get his passengers there quickly as possible.
I would recommend that you go to https://skyvector.com/ and create a flight plan.  It isn't too difficult, just click on "Flight Plan" in the top left corner and you should be able to figure out the rest.  

You obviously have some familiarity with ICAO airport identifiers, simply look for airports along the way that will keep you under a 886.7 NM leg length, and enter them one by one to build your route.  I would use a cruising speed of around 150KIAS based on a quick Google search of Twin Otter performance.  The website will calculate the times for each leg based on this airspeed.

As far as researching suitable airfields that can provide fuel and other services, that will take quite a bit of additional work.  I don't have a handy reference for you, but you could start by searching for World or Latin American Airport Directories.  I wouldn't expect anyone here to do all that work for you and post it as an answer.  If you have any detailed questions as you go don't be afraid to ask. 

Regarding your questions about avoiding immigration authorities, that's up to your fertile imagination to come up with fictional scenarios.  There is no aviation specific way to answer this, and most people would be hesitant to recommend methods to circumvent the law.