I would wear it with dark wash jeans and a bright colored tank top or t-shirt on the weekends. If you are really worried about it being to "granny" wear it with an ironic slogan t-shirt or put a couple of those edgy buttons you can get at a Hot Topic to add to the shrug itself.
Grey is such a great neutral color that the shrug would go with almost anything.
As for the sleeves, I like them.
Just go for it!