I was flying a very low time Cessna T206H the other day, including many circuits. I experimented with shimmy avoidance in mind. In this aircraft, with full fuel, and two of us in the front seats, it was easily possible to raise the nosewheel off the surface at 25 MPH indicated, and hold it there with no difficulty, controlling the takeoff form there from the mains only. Extended flaps and partial power, with full up elevator was used, and then right rudder to keep it straight with the application of the rest of the power. Similarly, landing, there was no problem holding the nosewheel off to happily slow speeds, while controlling direction with rudder only.
During the same customer service, I also flew a few circuits in a Cessna R172K. Prior to the flying, I found that the nose gear steering collar and shimmy damper attachments were as loose as I would tolerate. Similarly, I held the nose light, and the flying was fine. I reported to the maintainer my recommendation that the oleo steering be serviced.