You can use either. The panniers will not interfere with the wireless signal. Some people complain that wireless is more subject to interference, but this is a small problem. I use a wired computer for touring, just because it's one less battery to worry about. But that's a very small issue too. I use a wireless computer on my daily bike. Flip a coin.
I agree on all of that except interference being a very small issue. My two companions on the TA found their wireless ones quite annoying. The biggest culprit was interference from neon signs when parked in front of stores or diners. The wireless computers would often register miles while the bikes were parked. The other issue was that like many other wireless models they needed to be turned on before they started working. Forgetting to turn them on until down the road a ways offset the mileage registered while sitting still
They also got crazy readings sometimes when near power lines, electric fences, and broadcast towers. They might look down and see a 700 mph reading once in a while.
I gave up on wireless long before I started touring so I have never toured with wireless, but I had the same problems with several different brand name models before giving up on wireless ones.
The total miles traveled were not off by much on the Trans America, but my companions were pretty annoyed by the little differences that made it difficult to keep track of things like how far the next turn was.
One of my TA companions, went into Performance after the Trans America and when the sales guy asked how her tour went and how the gear he sold her worked out, she said "Great except this P.O.S wireless computer you sold me". His response was "I could have told you that, all the wireless ones have those kind of problems". He then gave her a refund that was used to purchase a wired model.
My recommendation is that if you use the computer to keep track of your turns throughout the day base on mileage from the start, stick with a wired model. If you are worried about breaking the wire some of the MTB models have a heavier duty wire.