I just have to say, that's actually a really interesting idea for a trapper build. Might I ask what other skills you're bringing (specifically, which traps)? I'd advise Flame Trap, since burning is the highest dps condition out of them all, and something that does bleeding (such as barbed trap). Since you're going to be relying on damage-over-time to kill off enemies, and not simple spike damage, you'll want some defense for yourself too; namely, some dodging stances to remain alive while your enemies burn to death. Whirling Defense, Dodge, and Zojun's Haste come to mind here. You could also use Tripwire (NF) so that enemies have to endure a second or so of complete helplessness on the ground in which the burn+bleed can really do damage. So we have:
Archer's Signet, Barbed Trap, Flame Trap, Dust Trap, Tripwire, Whirling Defense, Dodge, (something else).
In answer to your original question, as Toraen said, all duration modifiers in GW take effect when the related effect takes place. So if your modifier on your sword is "Enchants last 20% longer", you want that sword equipped when you cast your enchantment in order for that to take affect.