A 12 inch wheel is the absolute smallest you can go, for an adult rat. It's better if you can get a custom made one that's larger. You can get 16", "homemade" wheels on Ebay. They're listed for chinchillas, but rats love them too.
You might want to try a "saucer" type wheel. You'll still need one that's 12 inches, but they also come in 14 inches.
Don't worry about the "silly factor"... If your rat/s enjoy having a wheel, it's what they like, not what you like.
Not all rats like or use a wheel. The ones that do like a wheel don't care what they look like. Just make sure, if you get a wheel, it's large enough to accommodate an adult rat.