I too used to hate wrapping, then I learned how (company merger forced me to do gift wrapping as part of my new job), and actually enjoy it now. At one time I even played with the idea of opening my own gift wrapping business. When the ladies of church have their seceret sister, I can never wrap my gifts because everyone knows that they are mine! It is pretty irritating - I always have to use a gift bag.
However, I completely understand the time factor. Since you are a crafty person, maybe make some really cute bags to put them in. It could become a family tradition or game. Who gets the Santa bag this year? What do you think it is, look at the shape. Or, that is my bag (name embroidered on it), I will try to guess what is in it. Good luck.