The need to hold things comes with habit, not HRT, if you ask me. I, for instance, have always had that need to carry things around, because I've always had a school bag and books when I grew up; always a sort of bag to carry, or something. And I've pretty much always felt awkward, wondering where to put my hands, when I don't have anything to hold. I haven't noticed any change, really.
I guess since you started using a purse, the habit got into you as well.