I know this is basically dead but still it would be cool to see a melee attack only challenge

While this would be cool, it's unfortunately impossible. To defeat the Dweller-in-Darkness, you must use abilities or weaponry in general

This could work with a challenge run where you use melee attacks as much as possible though

One idea would be to use only melee combat and remove the boss fight from the rating so you can use weapons against it

From memory, the only times you need to use weapons are when the Guardians are fighting the Dweller, and also Fin Fang Foom.

For a challenge run like this, you could use abilities/weapons to build up their stagger bars, and then use melee attacks when they're weakened. Apart from these times, it's mostly smaller enemies that are around to defeat

So a near only melee run is definitely possible