Have the challenges be unavaible until the second round of play.
I dont own the Onyx Edition, but I own the standard "Revised Edition" which mainly plays exactly the same.
When you say "New Onyx Rule," do you mean that it is an official rule in the instructions manual ?
If so, when did this "new rule" come out ?
Or do you mean that it is a "new rule" that you are proposing (a house rule) ?
I have actually played with this rule with my Risk Revised Edition for some time now.
I think somewhere else I read, that the Onyx Edition official rules say that you could have players turn-in one card in order to take one objective (and this helps to "level the playing field"). So when taking an objective, not only do you not get to draw a new card, but you must also have a card and relinguish it, to take the objective.
Do you see this rule in your official instruction manual for the Onyx Edition ?