A good question.
Unarmed Strikes are certainly listed as a type of weapon, but it's less clear when they count as wielded or not. This has been previously debated, and I don't think it ever got clarified by the devs.
Ultimately, as a GM I'd allow it, as you're not getting anything that weapons couldn't accomplish.
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From the core rule book page 168
You can attack with a weapon (or threaten an area with it,
for all melee weapons except unarmed strikes) only if you are
wielding it with the correct number of hands.
From the core rule book page 243
Wielding Weapons
When the rules refer to wielding a weapon, it means you are
holding a weapon with the correct number of hands and can
thus make attacks with it. For example, if you are holding a small
arm or one-handed melee weapon in a hand, you are considered
to be wielding the weapon. If you are carrying a longarm or
two-handed melee weapon in one hand or wearing a holstered
or sheathed weapon, you are not wielding that weapon.
Core rule book page 190
Unarmed Strike
An unarmed strike can be dealt with any limb or appendage.
Unarmed strikes deal nonlethal damage, and the damage
from an unarmed strike is considered weapon damage for
the purposes of effects that give you a bonus to weapon
damage rolls.
Planar Radiance (Su)
As a move action, you cause a weapon you wield to deal fire damage instead of its usual damage type. (This doesn’t change whether the weapon targets EAC or KAC).
Not 100% sure, but if they meant any attack, not just one with a wielded weapon, it would have been shorter to state: "As a move action, you cause your attack to deal fire damage instead."
Unlike unarmed strike, adaptive strike goes out of the way to state that it doesn't require a hand to wield and that you can threaten an area with it. There may be other cases like that but they seem to be exceptions to the rule.
Not sure if that's the answer or not, but that's the rules involved I could find.