First off, are you qualified for TSA PreCheck - if so you may not have to remove your shoes.
If not, simply tell the TSA at the WTMD that you can't remove your shoes for medical reasons. Period. They aren't your doctor, they don't get to tell you anything medical. They can perform additional screening, typically they will swab the shoes for the ETD magic box.
If they give you grief, ask - politely but firmly - for a supervisor (not a lead - 2 striper, but a supervisor - 3 striper). S/he should actually be aware of TSA policy.