No you don't.

You'll be fine. I would recommend getting to the airport a little bit early just in case they request that you check them.

They are not in violation of any of the TSA's policies, they are not in violation of any of the FAR's (Federal Aviation Regulations)

They COULD be considered a weapon, but so could many things. If they inquire as to what they are, simply tell them and explain that its like ski boots. If you're going on a ski vacation, you can check your skis because if they get lost you can simply rent another pair and your vaca isn't totally ruined. If your boots get lost though, since they are custom fitted, its much more difficult. Same with pedals, you have your shoes and pedals setup just right.

If you're taking your shoes, you might want to just clip them to the shoes and it may be easier to explain.

But I doubt if you'll have any issues.