If, like the question states, you are only interested in excluding #REF! errors, this is the correct check:
  For Each akt_range In Range("C3:J65")
    If CStr(akt_range.Value2) <> CStr(CVErr(xlErrRef)) Then
      akt_range.Value = akt_range.Value2
    End If
  Next
Technically, the above will fail in the very special case of a formula returning the error code string for #REF! exactly, e.g., ="Error 2023". The absolutely bulletproof check is this:
  For Each akt_range In Range("C3:J65")
    If Not IsError(akt_range.Value2) Or CStr(akt_range.Value2) <> CStr(CVErr(xlErrRef)) Then
      akt_range.Value = akt_range.Value2
    End If
  Next
If you wish to exclude all errors, a better solution would be to use .SpecialCells() to eliminate the errors from the range before looping:
  For Each akt_range In Range("C3:J65").SpecialCells(xlCellTypeFormulas, xlLogical + xlNumbers + xlTextValues)
    akt_range.Value = akt_range.Value2
  Next