Kevin managed to do DW without a trailer, in his Shelby, but he had a fastback and no fuel cell. I don't know, Alan; having a small trailer makes life so much easier, and keeps you from tearing up the interior. As long as you've got a good mount, you'll never know that trailer is back there, but it'll keep you from having to smash everything inside the car, which isn't fun if you ever have to hit the brakes hard.
When it comes to drag slicks on the street, I don't think it matters if you have bias ply or radials. They'll be fine in the rain....until they aren't. Then you'll likely be looking at the road from about 50', if you're not on your top. Maybe a check of the forecast right before will help make that decision?