I'm not sure this is a great idea, at least not for a conventional fighter.
Armor training will eventually get you +3 AC in relaxed dex limits, possibly more if that puts you over the threshold to use mithril full plate, though for a finesse build this is unlikely. Duelist will get you +Int. The next armor training is at level 7, just one level after you enter Duelist.
Weapon training will eventually get you +3 more to attack and damage. If +1 to hit is valued as +2 damage that's a mere 1 point short of Precise Strike's benefit, and is not precision damage.
Sticking with fighter gets you twice as many feats.
Supposing you're at 14 int duelist gets you a whopping +1 AC over fighter that goes away at level 11. Damage goes up at some levels because weapon training is a +3 damage equivalent chunk every few levels instead of a point per level.
Skill points go up, but you lose favored class. A benefit, but less of one that it looks like.
You get more class features than you lose feats, but the armor and weapon restrictions are going to prevent you from being all you can be.
If you have 13 or 14 strength I would consider using an Aldori Dueling Sword with a buckler and staying in Fighter. Splitting your enhancement bonus budget between a buckler and armor is comparable to Aldori Dueling Mastery and you can two hand for 1.5x strength and 3:1 power attack without losing the finesse property at the expense of -1 to attack rolls and your shield bonuse. If you'd always or almost always two hand the sword skip the buckler and consider Aldori Dueling Mastery for a +1 shield bonus.
If your GM is lenient you may be able to dervish dance with a buckler as it is arguably not carried since it leaves the hand completely free. This would still conflict with Canny Defense which uses the term "use" instead so this is another stay in fighter option. Unlike the Aldori option this cannot be two handed without losing the finesse quality.
For archetypes that give up either weapon or armor training Duelist may be more attractive.
