I think you were missing a few steps
Try this
Option Explicit
Sub Test()
Dim ws As Worksheet
Dim rText As Range
Dim y As Long
Dim fndList As Variant, rplcList As Variant
fndList = Array("C", "1", "C1", "C2", "")
rplcList = Array("Tom", "John", "Paul" & " " & "Smith", "Clarke", "Claire")
' Loop through each worksheet in ActiveWorkbook
For Each ws In ActiveWorkbook.Worksheets
'make sure that there are text values
Set rText = Nothing
On Error Resume Next
Set rText = ws.UsedRange.SpecialCells(xlCellTypeConstants, xlTextValues)
On Error GoTo 0
'if no text then go on to next sheet
If rText Is Nothing Then GoTo TryNextSheet
For y = LBound(fndList) To UBound(fndList)
'changed LookAt to xlWhole
rText.Replace What:=fndList(y), Replacement:=rplcList(y), _
LookAt:=xlWhole, SearchOrder:=xlByRows, MatchCase:=False, _
SearchFormat:=False, ReplaceFormat:=False
Next y
TryNextSheet:
Next
End Sub