You could number each girl gift 1 - 8?? and each boy gift 1 - 8?? or whatever. Then have the kids each pick a number, then they get the corresponding gift. If they get their own gift, you could do a quick change before they all open.
Make sure you have some extra boy and girl gifts just in case someone doesn't bring one. I'd hate for someone to be left out.
I can remember doing this once in 4th grade but I definately couldn't do it with my class. I teach in a poor rural community.
I place all the gifts under the class tree (or in a special spot in the room if you don't have a tree..). (boys gifts in one place, girls gifts in another) Then I pull a name from a hat. That child gets up and gets to pick one of the presents and bring it back to his or her seat... but do not open it.. as the child walks to get the gift, the rest of the class says (on the count of three..) Happy holidays (insert name!). Continue and pull names until all students have a gift at their seat. Then at the count of three all kids open gifts at the same time...... Yeah!!! such fun!!!
I sit all the boys in one spot and all the girls in one spot. The gifts are separated. I have a couple sets of dice in each group. If a kid rolls a double, they get to pick a gift from the group. After everyone has a gift, they continue rolling and they can "steal" from someone when they get a double. I have done this for years and they love it. You need to make sure they don't tell each other what they brought!
We used to play musical presents. Everyone sat in a circle (so you'd have a boy circle and a girl circle) and they hold their present. Then you start the music and they start rotating presents. You just have to watch one child in the group to see that that one kid doesn't get his/her own present and that should ensure no one else does either. So when the music stops (or you decide to stop it), they should each have a different gift and they can all open.