I am currently the custodian of two "cardboard dulcimers" which have been used in classes and as loaners for about 20 years. They still play well, although their cases are plastic bags. I used them two weeks ago to demonstrate the difference between C-G-G and D-A-A tuning on identical instruments.
I will emphasize that only the bodies are corrugated cardboard. The sticks are 1x2 lumber, and they have guitar fretwire frets, and regular tuners and strings.
A huge part of the true cost of making "a real dulcimer" is in the sanding-varnishing-sanding-varnishing of the wood body, and this has no effect on the sound.