For example: A were-creature only affected by Silver is hit with "PTD Eviscerate" and the PC did not call a silver carrier, would the creature take the Eviscerate?
Same goes with Disarm, Stun Limb, Shatter etc. The only example in the ARB is SLAY.
Yes, all PTD skills should be called with their appropriate carrier. A creature only affected by Silver would call "No effect" to the "PTD Eviscerate".
"Prepare to die, Silver Eviscerate!" is the proper call.
For reference, see the description of "Slay" on page 67 of the 1.2 ARB (PDF):
For example: Terin is using a magic
sword. He is fighting a vampire, which can only
be harmed by silver or magical weapons. He
calls out “50 Magic Slay.”...When first activating the
skill, the character must say “Prepare to die!”
In general, you can assume that all PTD skills work the same. If a description of a skill is lacking under one PTD skill's definition, but provided under another PTD skill, it will apply unless otherwise specifically noted.