Not clear about what you're asking. Are you talking about some extra baggage or a large air cargo shipment delivered to the airport? I guess I'm not clear on why you couldn't simply pick it up at the airport yourself- you'll have to go there to clear customs anyway. Don't have a car, too much for a taxi? You can rent a truck, cargo van, or even moving van (e.g. U-Haul) to pick it up, if you are (or know) a licensed driver (and feel confident driving the vehicle).
If you can't do it yourself, if it IS a large shipment that just needs to be moved within the city itself, you do not need a "shipping" company, but a "moving" company, and it will probably be expensive. It all depends on the size (volume, not weight) of the goods to be moved.
You can Google "Vancouver moving companies." Don't be afraid of smaller companies - Where I lived before in the States, there was "Two Men and a Truck" who were perfect for moving jobs that were too big for me to do by myself, but too small to warrant the expense of a full-fledged moving company. If you find a company that you're interested in, try to find online reviews from previous customers...