both my kids were early (10 mos) independant walkers. they understand alot more than what they can say. the best thing i can tell you is to explain everything to her..... "when we walk to daycare we need to stay on the sidewalk, so cars can see us,and that we don't get hurt". "we can't touch that bush because it has thorns and it will hurt". i've even held it out and let my daughter touch one of the thorns on her finger to feel it..... now whenever we walk by something she says "becareful mommy, this bush hurts" (she's now 3).
you just need to walk/talk her through it. try to make a game out of holding hands... sing a song, so it's like your dancing... see if she'll take to that.
you say you're not a leash fan, but it might be soemthing that you need to do. Get a little backpack that she can wear to carry her own stuff to daycare (or she can put anything into it) but it will give you a little something extra to grab onto if she starts to wander to far. and you could put a leash to the handle on the top. i got my kids the eddie bauer stuffed animal leash backpack. my daughter loves dogs so i got her the puppy one. i used to put it on her so the puppy was over 1 shoulder. she used to talk to it like it was her friend, and narrate everything that she was doing. you may not want to do it, but it's soemthing that will let her have the freedom she needs to feel, but also alows you to have a little control over her (so she can't run off into the street, or run away when you are shopping). it does come in handy if you are having a second anytime soon. my kids are 23 mos apart, and that was her opportune time to run away when i was with the baby.