Hyperlink is a character style so I don't really know why you would have applied it to the paragraph marks in the first place:
Code:
Sub ScratchMacro()
'A basic Word macro coded by Greg Maxey
Dim oRng As Range
Selection.Find.ClearFormatting
Selection.Find.Replacement.ClearFormatting
Set oRng = ActiveDocument.Range
With oRng.Find
.Text = "^p"
.Style = "Hyperlink"
While .Execute
oRng.Select
Selection.ClearCharacterAllFormatting
oRng.Collapse wdCollapseEnd
Wend
End With
lbl_Exit:
Exit Sub
End Sub