Thank you both for your thoughts. It's not the answer for me yet though. You may not remember, but I originally said;
I have verified that it works if you use the File.. Manage.. Value Lists route, but I don't give any of the users access to this menu. I have considered the option of using a script to open this setting, but I want to maintain the look of my user interface and don't want the back-end to show.
I still feel this way!
I have to say, I really don't understand the implementation of the privileges for value lists, however I'm resigned to the fact that I can't use them the way I want to. I think, instead, I'm going to create a new table for the categories and a new layout for editing them. I'll then simply script access to that such that only administrators can get to it. It's a very long way round of achieving the same thing, I think.
Anyway, thanks very much for your help - I hadn't anticipated that it would come so quickly!