Tyzias was a lot more thorough about searching than Dust was. His strategy for dealing with traps was 'trigger them, then evade or counter as necessary'.

"Right. Would it be too cliche in exchange to suggest I go first?"

Tyzias can almost certainly handle herself; every instinct of Dust's told him that. But so can he, and he wasn't in the least bit hesitant to get his swords involved and give his athletic fighting style a workout, plus if he was the frontliner Tyzias could cast spells into the fray for his Dust Storm to amplify.