Well, when you purchase a servo new, it would not be capable of continuous rotation. But if it already can rotate continuously, then you do not need any further modification. It should be fine.
As for the wheel . . .
Unless you can find a wheel that is specifically designed for servos (let me know if you find any because I have not), you MUST drill into your wheel. You only need to drill 2 holes, can't be that hard. Measure and mark off the holes, and then just get a hand drill or a dremel. If you don't have one, I am sure a friend would. I used a table top drill press for nicely aligned holes, but it really does not require high accuracy at all. Shouldnt take more than 5-10 minutes per wheel.
My pictures showed two examples with two very different wheels.