Can I put my regular smoked sausage in a dehydrator and have it come out okay? Safe to eat?

I was a given some smoked links from a THF friend. They were honestly already too dry for the dishes that I used them in, including gumbo.

I'd say depends somewhat on what preservatives/curing salt etc. was used in them. If you don't know or cant find out I probably wouldn't.

Is it precooked or uncooked? If uncooked just be sure to bring it up to temp. You will need to check with a thermometer.
If precooked, you are good to dry in the smoker.

Also any sausage with cheese will probably just melt out the cheese. If it is precooked it will most likely not be high temp cheese and it will melt out completely.
Commercial processed sausage is typically precooked meat and the cheese is low temp.
Most wild game processors will use high temp cheese if the meat in the sausage is uncooked.