However, in the final fight (even though he's now wearing the mask)...
It's unclear what the mask brings to the wearer other than raising people from the dead. The voice over in the beginning of the film specifically states that the mask is a tool for resurrection. Then, it says that, "The mask summoned spirits of unspeakable evil, given them (the wearer) power no mortal man should possess."
This could refer to the mask's power in allowing man the power of resurrection--or, it could mean the mask has other powers.
If the mask is only about resurrection, what you speak of makes sense because the mask wouldn't give Zym extra fighting skills or sorcerous power to fight Conan.
Maybe, Zym has to wear it until the resurrection is complete.
I never had the sense that Conan was ever in any real danger.
Yes. This is one of the failings of the film.
Maybe in his case, the title doesn't say about anything about his skills or powers, but really is just his rank.
And that shadow thing could be something rather mundane. The Black Prince probably got the name just by having a black crest. Erik the Red probably simply had red hair.
Maybe the Shadow Lord is just the Lord of a castle that lies in a valley surrounded by high mountains, so the sun rarely reaches it.
I'm not thinking in that direction because of the way Artus (Conan's buddy who is Captain of the Hornet) speaks of Zym.
"Zym? Do you know who that is? I am told that he is the Angel of Death."
And, before this, when Conan finds out Zym's name, the man with the sliced nose speaks of him thusly, "He's a legend now, a Shadow Lord."
Conan replies, "A Shadow Lord, huh? Speak."
No-nose speaks of Zym as "a" Shadow Lord, not "the" Shadow Lord, leading one to believe that there is, or has been, more than one of them.
And, Conan, in his reply, has obviously heard of the Shadow Lords before, but not Zym himself.