Our local food pantry does a shoebox related thing, but for homeless people. They ask you to buy things like toothpaste, deo, shampoo, plastic silverware, etc and put them in a shoebox. You can customize it for a man, woman or child - they just ask that you label them. Maybe check with your local food pantry or other service provider.
ETA: I don't even think it's a Christmas only type thing, but rather an all year round thing with them.
I'm not sure where you live, but I did a search on google for "shoebox homeless" and came up with a few links like:
There's -
http://www.shoeboxministry.org/ (by the title they seem like maybe they'd be Christian, but that doesn't seem to be the focus)
http://www.some.org/inv_holiday.html#drivewww.operationshoebox.com does it for service members - perhaps there's a local group near you?
From the links that I saw it also seems like some United Way groups do the same thing. I'd try checking with your local United Way. I'm glad our local food pantry does it because I didn't want to to it through Samaritan's Purse either.
If there isn't an established group doing something like this in your community, like onlygirls suggested, maybe you can get in contact with local shelters (women's/homeless/etc) to see if they'd be willing to accept donations like this. Maybe you could get other friends/family to help so it'd be more than just a couple of boxes or something?