Unholy Writ cannot be used on my hero before it gets shuffled, right?
Thanks!
Correct. "Triggered" Artifacts (like HT) activate before "conditional" Artifacts (like UW) have a chance to. A triggered Artifact is one where something happens due to a trigger, in this case, when your lone prophet enters battle (trigger) then something happens (the option of discarding or playing an enhancement is given). A conditional Artifact is one that can be performed at any time that the condition is met (A Hero is in battle is UW's condition), except for carrying out an instantaneous triggered ability.
