Yep. Per the PHB, your worn outfit does not count towards your own encumbrance (though it does count when determining how much encumbrance another guy has if he tries carrying you around).
I track encumbrance usually (and always when I'm playing, not DMing).
Anyway, I tried analyzing a low-level Swordsage versus a low-level Fighter (well, a Swordsage 1 who goes to Fighter 2, then back to Swordsage, compared to a pure Fighter). Turns out that, unless you got 17 or 18 Dex and Str both, they're evenly matched for several levels if you interpret Shadow Blade as 'Dex to damage alongside Str' (though I normally interpret it as 'Dex to damage instead of Str').
I used a spiked chain comparison, and it turned out that the Swordsage had a bit more AC at 2nd-level, but the Fighter could Power Attack for 2 more points of damage around 3rd or 5th level (it wasn't until 4th that the Swordsage 2/Fighter 2 got their Wis to AC ability, so until then they'd be wearing the same armor as the Fighter; the Fighter could Power Attack sooner, when the Swordsage/Fighter was using Combat Expertise, but it evened out again after that).
At upper levels it would certainly be in the Swordsage's favor with Shadow Blade adding Dex to damage along with Str to damage, but not before 10th or 12th level probably, when they'd have enough wealth for the right magic item combos for more Dex and Str (can't use Gauntlets of Ogre Power at the same time as Gloves of Dexterity, so they'd have to be able to afford a Belt of Giant Strength +4 before they could get both abilities boosted enough). The Fighter's Greater Weapon Focus and Greater Weapon Specialization would make up for some of it, and at certain levels his extra Power Attack potential from higher Base Attack Bonus (and the GWF's attack bonus allowing him to spend more on PA without missing too often) wins out, but eventually the Swordsage X/Fighter 2 may be more damaging with Shadow Blade, since neither can afford to Power Attack too much lest they miss far too often on the attack.
Especially since the Swordsage will be using lots of maneuvers (which will yield more bonus damage than Power Attack sometimes, and without any of the reduction in attack bonus).
So..... If not for the fact that Swordsages can do even more damage with maneuvers than Fighters could, it would be fine until upper levels to let Shadow Blade be interpreted as 'Dex to damage alongside Str'. But the maneuvers make it too much, considering the Swordsage is much more capable outside of battle (and has more useful skills for battle too, like Tumble) and will often do more damage through maneuvers. Being able to add Shadow Blade's Dex to damage alongside Str will probably be too much.
Without that extra damage, they're probably fine alongside Fighters. So I'm inclined to consider Shadow Blade is meant to be interpreted as 'Dex instead of Str for damage'.
