The security people at most airports in the US do NOT ask people to remove shoes that are thin-soled, but do ask everybody wearing thick soles and tennis shoes to remove them. You might consider telling the security people that you have a problem with balance and fall very easily, and ask that you be allowed to sit down while removing your shoes.
I have a pacemaker and security can be a nightmare or very simple, depending upon the people at the security checks. They have me stand aside and get a woman guard (I'm a woman) over to help me. My problem is that when I travel alone there is nobody to go through security first and get my purse and carry-on off the conveyor belt for me, which means that unless the security person gets my things ANYBODY can help himself to my stuff! Sheesh!
My brother-in-law was hurt in England a couple of years ago, and the doctor told him to purchase and use a cane, which wasn't a problem at all until we arrived in New York. The security people certainly needed to put the cane through the x-ray, but told him to walk through without it and pick it up at the other end! He asked them to fetch the cane after it was x-rayed and hand it to him so he could walk, and they said NO! At that point a very old lady with a walker came up for security, and my sister pointed to her and asked the security people if they intended to make her crawl through. The security man decided to return the cane to Tom.
Although security is extremely important, I believe the security personnel should be reminded of and instructed on the Americans With Disabilities Act, which states that people with disabilities cannot be denied access and services, and that reasonable accommodation must be provided. Because of my pacemaker, I cannot go through security machines, and have only had one problem with that. I was at the local courthouse to register my teaching certificates, and was told that I couldn't enter the courthouse unless I went through the machine. I had a pacemaker ID card (and even offered to show them my scar), and asked that they frisk me instead. They refused, and I asked to see a supervisor. Same song and dance! I then asked to speak to a police officer standing nearby. Same song and dance! At that point I suggested that he call upstairs to the State's Attoryney's Office, get one of the assistants on the phone, and tell them there was a lady they were denying access to a public building because she was disabled and couldn't go through their machine, and ask how that might square with the Americans With Disabilities Act. The officer made the call, turned white, and immediately apologised to me. I told him he was welcomed to frisk me without calling a female officer, and he said that wouldn't be necessary at all. He called another officer to come to the front door area and escorted me to the office to get my certificates registered, apologizing all the way. I suggested they establish some alternative security procedures for people who can't go through the usual security, and he said that would be done within 24 hours, which was what the State's Attorney's Office suggested as well. Had I been denied access I was going to make two phone calls -- one to my attorney and another to the local newspaper. Sheesh!