Welcome aboard emontherun, a CMS system of ANY kind is designed so you can modify content without breaking the web site - just like you say here.
... but do not want to try to put our site into a program and then destroy it ...
Why would you take on something you have no idea how to manage? CMS systems are made for people **just like you.** That's not a flame or an attack, you have better things to do with your time than learn all the tech stuff, don't you?
If it's a true non profit, you need an intern.
There are thousands of high school and college kids just begging to work on this stuff. Find a couple and manage them. They get school credits, you get to learn a little of what they've learned.
The short story IMO is Dreamweaver creates horribly hard to maintain and update pages. Whoever told you this is oversimplifying your plight. Put your effort into tweaking the CMS to meet your end, the site will survive it and everyone goes home happy. :-)