I am the owner of the Pucon Kayak Hostel
and would be happy to help you with any logistics.
First, let's see if we can answer some of your concerns. if you choose both Pucon and Futa you will have to consider how to get to the Futa.
A. Drive through Argentina or,
B. Take the Puerto Montt to Chaiten ferry.
Both are fantastic experiences and will offer adventure stories. There are pros and cons to both: like an overnight ferry can be more relaxing but may costs more money if your driving. While, driving through Argentina requires exact paperwork and many have been turned back at the border for this reason.
Pucon has a few good class III options in the area. For example Pucon Kayak Hostel has a put in for the Lower Trancura (class III) and a take out for the Upper Trancura right at the riverside base. The Liucura, San Pedro, and Lower Fuy are other day options for class III boaters. The Upper Maichin has an easy class II section for the beginner beginner.
If you need kayak rentals or a fun place to stay then I invite you to consider Pucon Kayak Hostel
as an option.