But... There's a sword right there.

Maybe he failed a spot check.

He tried to reach the thing, but he realized his flaw would activate, too far away.

that made me laugh loudly

Oh, come on, it's not hard. You just break it down into twenty smaller trips, and rest at each "camp", always headed roughly in the same direction.

I have seen this happen. "I travel ten feet forward, and draw an arrow pointing forward in the ground."

"Umm, okay..."

"Excellent! Now I lie down and take a nap."

"Okay."

"When I wake up, I follow the arrow, and walk another ten feet."

The DM let him, because it was both dumber and more time consuming than taking a guide.

He'd still be subject to the one obligatory random encounter

I call this encounter "the most confused band of kobolds ever".

"While you were asleep, you rolled around and smudged out the arrows."

Bah, they are all playing dead. All swords and guns deal non-lethal damage here. Except when bad guys use them.