In my local sorority, we did gifts for our big/little sisters. I decorated a paddle for my big; she decorated a wooden cut-out figure for me, with our names and letters. (I still have it - with an AEPhi ribbon on it
) My pledge sisters and I also made up a paddle for our pledge mom.
AEPhi nationally doesn't allow "paddles" per se, but does encourage gifts. I think I bought letters and a couple of small gifts for my little. I also made up a cross stitch of the AEPhi letters and a lily of the valley for my big, and another for myself. I meant to make one for my little, too, but never got around to it...
In my book, a paddle is just something you can decorate and give as a gift - provided it's not actually used for paddling. It's the act that's hazing - not the object.