Does Martial Arts Damage Apply to Ranged Attacks with Monk Weapons?

Inspired by an answer to What is the Attack Roll for Deflect Missile?.

The Monk’s Martial Arts feature states that monk weapons are, “…short swords and any simple melee weapons that don’t have the two-handed or heavy property.” (emphasis mine)

For the purposes of my question, I am assuming a 17th level Monk, so that the Martial Arts damage die is 1d10.

My question is that when making a damage roll with a weapon that can be either melee or ranged, like a dagger, which damage die do I roll on a hit for a ranged attack? I am assuming this uses 1d4 because this isn’t a simple melee weapon anymore, but a simple ranged weapon based on the definitions for melee and ranged weapons as defined on page 146 of the PHB:

“A melee weapon is used to attack a target within 5 feet of you, whereas a ranged weapon is used to attack a target at a distance.” (emphasis from the PHB)