Full transposition of superconducting wires within a conductor may not be a requirement for high temperature superconductor (HTS) magnet for fusion applications. Already, conduction-cooled 20 T model coil built with non-transposed HTS stacks has been demonstrated by Commonwealth Fusion Systems (CFS). Here, we discuss 3 possible stacked HTS cryogen-cooled conductor concepts for toroidal field (TF) magnet applications. The first one is somewhat like LTS conductors, the second, HTS stacks are capped by copper stabilizer, the last one, only stacks without copper. We simulate a simplified TF magnet model, 12 T, size of KSTAR, using the 3 conceptual HTS conductor designs. A comparative thermo-hydraulic analysis for a fast charging case has been carried out and its implications on HTS conductor design are further discussed.