Hmm looks like I was wrong. In looking at the underlying data, ALL the perks you listed require a melee or unarmed WEAPON to be equipped to work - UNLESS "IsWeaponSkillType Unarmed" is true with no weapon equipped, which I don't think it is. Might wanna use Brass Knuckles.
It'll have to go from a perk by perk basis, I guess. The descriptions are all blotched, and so far despite what you've found, my results thus far have yielded a different conclusion.
I haven't checked the perks in the GECK yet, though with some testing, Piercing Strike benefits unarmed attacks without an unarmed
weapon equipped, and it was worded in the description to benefit melee attacks, appropriately. On armored targets, it displays the armor penetration icon, along with a significant damage increase. (At level 1 with 1 luk, it consistently took 40-41 punches to remove a bar of health from the alpha deathclaw male, as opposed to the several hundred punches without it that I'm not patient enough to carry out complete testing with (I haven't gotten him down a bar without piercing strike, yet, lol).
Going to test the others; which leads me to my next question: Is there a console command to check an NPC's health? :shrug: In any case, I'm probably going to report all of this to the bug section since unarmed perks are kind of sketchy as it is.
edit: Tested purifier, with piercing strike to maintain my sanity. Consistently, it took 26-27 punches to remove a bar of health, leading me to believe Purifier works without a weapon, despite the fact it's worded to only work with an unarmed weapon.
edit #2: Tested, super slam, works without a weapon, worded with unarmed attacks.
edit #3: Testing Slayer, but a 30% increase is difficult to spot. (I added the perk via console, and am simply watching the animation speed with unarmed and with brass knuckles) It seems like Torm is correct that it doesn't work without an unarmed weapon equipped, but it's still kind of hard to tell.
I can't really test Ninja, especially considering it's bugged as is. I guess at this point I can conclude that most unarmed perks without a weapon equipped work. Slayer is bugged, unless it was otherwise intended that the benefits of unarmed perks should only be received whilst wearing an unarmed weapon.