NSN for watches all start with the 6645 class code. The serial number is on the bottom, and that 67 is most likely the fiscal year. You can also check the movement number against an online Hamilton list and it'll be pretty close to 1967.
The actual NSN is 6645005267374. What's engraved on the watch is the Federal Stock Number. That NSN was canceled in 1998, according to the Defense Logistics Agency database... and the government paid about $80 for that watch when it was last procured.
In any event, the watch and the cardboard box don't match. The wooden box also might not match.
Tom