Tim, sorry I don't know of a shop in your area. However part of the Corvette experience is a little do it yourself. Changing the oil is one of those easy tasks that does not require too big of an investment in equipment. Just remember safety is paramount but you can change the oil in most Corvettes in a half hour or so. Maybe longer if you start cleaning under the car.
If you have a Mobil 1 Express or another decent Lube shop that has good reviews, I would take it there if I didn't want to do it myself. Like Murray said, It's not difficult and the express lubes are in and out while you wait so you know they aren't out joyriding at lunch time.
Sorry I can't be of more help, as I live a bit far from yourself, I don't know Ottawa too well, and like others, change the oil myself as part of the bonding experience with my car.
If I were to have someone change the oil, as Rruff stated, a very well respected lube shop may be an option as no one is driving your car. There's no grease nipples on your car, unless you have a Z51, then there are two on the rear end links. Actually it's one of the very rare Corvettes in the last 20 years to have grease nipples. Anyway, hopefully someone will chime in with a shop they trust as we can't all be changing the oil ourselves.
There are too many yahoos in the oil change business for my liking so I just do my own. Ask around and you will probably find a good shop. One man operations tend to be the best from my experience. I've heard too many horror stories of not tightening the drain plug, to forgetting to put the oil in. Unless you are right there, you can't even be sure that you are getting the good oil that you are paying for. Just don't jack the car up at one corner and crawl underneath and especially on a dirt or gravel driveway. I worked with a guy who had his car jacked up and it fell on him. You are dead for a loooooong time.
I just bought my first Vette and am taking it to Getty Automotive, on Canotek Rd.
He comes very highly recommended by the Corvette community in Ottawa.
He is very busy, and you'll need to make an appointment with him, but the reviews online are ALL good. He is actually a Volvo specialist, but also works on Vette's as well, as he owns one.