Regarding this, for instance, I allow the characters involved in a Hazard (the Hunters, the Scouts, etc.) to invoke a Trait to approach the Hazard using a different Common Skill, after I've described the situation they find.
For example, let's say that the rolls for Hazard, role affected and consequence say that the Scouts find are the oes affected by a Hazard. They have to roll Explore or get Weary for the remainder of the Journey.
That's the "mechanical" part.
My narrative is that they've found a river that can't be crossed, and need to walk upstream and downstream looking for another way, which could make them Weary because of the extra effort.
Then it's the players' turn. One of them has the Trait Swimming, and explains how he wants to tie a rope to his waist, and swimm across the river, so that his comrades can cross it by holding the rope. We agree he can roll Athletics instead of Explore to overcome that Hazard, while the other Scouts can still roll Explore as usual.
This way the players inventive and initiative is allowed to come into play, and the characters they created become more important than just a "who has a highest Explore/Hunting/Awareness/Travel rating?".