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M'yeah but doesn't it kind of break the fourth wall or something like that? I suppose a lot depends on your group's style and I think my own group would be happy with it, tbh (we have no problem with breaking play for lengthy rules discussions, for example). But it really rather ruins it for me.
That right there is your problem. You've got a playstyle gap between yourself and the players on this issue.
If all your players prefer it to be transparent then that's how I'd suggest you run it. At the same time I'd look for ways to find enjoyment in Skill Challenges even if you must run them transparently for the sake of the group. I'd imagine that you are not running so many Skill Challenges that you'd feel that it ruined the game as a whole for you.
On the other hand if you feel like it's a total dealbreaker then you can lay down the law about it. But generally I'd vote for a majority rules philosophy about stuff like this.