Actually, I just checked and unless there was an errata, I would need to be Swordsage 3 in order to get the 3rd level assassin's stance.
Only if you start with Swordsage levels. If you take other levels first, your initiator level goes up, so you can take Assassin's Stance at SS 2. For example, a Factotum 4/Swordsage 1 has an initiator level of 3 (which would be enough to do it, except that your first stance must always be a level 1 stance). A Factotum 4/Swordsage 2 would have an initiator level of 4, which is plenty. For this reason, it's best to take your Swordsage levels as late as possible in the build.
Also why unarmed? I mean it would certainly make me more versatile, but if I'm using a bow for the majority of my fights why not make the best of it?
Because Unarmed Swordsage loses light armor proficiency (which you already have anyway) to get unarmed strike damage like a Monk. It might not come up much, but having it is handy. There's always the possibility that the DM will decide to leave you chained up and unarmed some where. Being able to use Escape Artist (boosted by your Factotum abilities) to pop out of the chains, then use a Mountain Hammer strike to punch through walls... well that's a handy way to escape.
JaronK