That is a tough one. It would be nice to have a helm with both Pierce and Shadow, but the truth is that a Max Shadow UV is incomparable to 5* defense. When in T3, Max Shadow will do almost nothing to reduce damage taken. For example, Shadow Max on Vog reduces Strata 6 Howlitzer attacks from 7.5 to 7 pips of damage per hit, and Zombies (half Shadow) are reduced from 8 to 7.5. Much better off with a Poison Max which is equivalent to a 5* armor's status resist.
Shields last longer by either getting status or damage, so I'd prefer status since almost every is going to be doing poison damage vs only half the things doing some specific damage type. Here's my hypothetical best...
Skolver UV Poison Max
Radiant Silvermail UV Poison Max
Barb Thorn Shield UV Poison Max
Divine Avenger UV ASI VH
Final Flourish UV CTR VH
Shivermist UV CTR VH
Polaris UV ASI VH
Sword Damage Trinket
Sword Speed Trinket
On the test server I tried both BTS and Dread Skelly and found that BTS was sufficient against undead areas and, of course, lasted much longer for beasts. Either is fine though. The BTS's damage bonus also means you can swap out a damage trinket for something else and still hit max. Max CTR on the FF is useful for tearing into Alphas. The DA's ASI is just to allow fast shielding when facing down many Kats.
This is serious overkill for UGWW :) But it would be quite ideal.
Once you get hit you get poisoned, once you get poisoned your extra defenses will matter less than they already do as such i believe you should max poison first then go for defenses. A max poison uv somewhere should do a lot coupled with radiant silvermail which Im not sure helps as many monsters do split damage on tier3, you'd have to test unless someone knows already. In that sens you could technically do with skelly set piercing max or skolver poison max
Id go with polaris to cancel the turrets
why shadow swords? piercing or divine avenger