Can you use unstoppable nanites on a melee weapon?
It seems like you can, especially since the rules say you can use it on a weapon that doesn't have charges.
But this get sticky when you read boost, "Boosting a weapon more than once before firing it doesn’t have any extra effect, and the extra charge dissipates if the weapon is not fired by the end of your next turn."
It keeps talking about 'firing' and you don't really fire a melee weapon.
Although, you can just as easily say the extra charge dissipates by the end of your next turn, because the 'firing' really does nothing rules-wise.
So i'm saying 'yes', but it seems boost wasn't meant for melee weapons.
You can already use variant boost on solar melee weapons. I don't think it needs clarification, you get the one attack boosted.