I could be wrong, but I don't recall an early NM .357 in an old model box with the NM sticker. I've only seen those with the Single Sixes and the 7.5" .45 and .30 Blackhawks. But regardless, with that serial number, you'd want the thin orangish-red one-piece box. Those were only made in 2 sizes and printed with standard auto info on the short one, and 6.5" .357 info on the long one. Every other handgun shipped in those boxes needed a sticker with the actual info for the gun that was stuck over the printed end. So I would think your correct box would be the short one with a BN34 sticker.
The few early 9.5" Single Sixes were shipped in plain white or brown boxes with a sticker. As were the first 10.5" tapered barrel Super Blackhawks (model S410), which interestingly used a split seam shipper reminiscent of the ones used in the 1950's. When the yellow & black one-piece NM boxes were made, they made a longer one for the long barrel guns, including the 10" barrel Mark II pistols.