As he was left with few invisibility talismans, Whittaker decided to save them for an opportune time. These will be extremely useful in a situation where he has to run away from a group of contestant killers or a horde of beasts.
From the previous battle, he had realized that invisibility talisman didn't help make a sneak attack if the other party have a mana sensing skill. Similarly, he also clearly knows that he was strong enough to battle D-rank and maybe even C-rank mages and battle master. That's why he didn't take extra precautions.
Walking alone in the Grand Canyon did not require much time before he was targeted by a dangerous opponent. Although he was Devansha's vision, Whittaker did not notice that person who was staring at his youthful face with the intention to fight and kill.