I'm not sure why you're saying that disability isn't an option. How thoroughly have you looked into it? It can be a frustrating, time-consuming process, but there are people called "disability specialists" who can assist you through it.
i would get a doctor's note that way you are covered. but if the job desc
Go to the principal or director or whatever and just tell them. Make the point that you might need to keep a seat nearby or even use a cane for support. Tell them that you would be glad to have your doctor verify the issues if necessary and that you are not wanting to come across as lazy, but that your physical needs are real.
Odds are this isn't the first time a teacher or parapro has had to deal with something like that. And the people in charge are human, after all. Just be respectful and let them know that you are willing to do your job to the best of your ability. It could even be that you could use a wheelchair or whatever. It shouldn't be that hard to accommodate you....teachers teach with broken legs and various health issues. it could be that they would even have some suggestions.
Yes, get documentation from your doctor stating exactly how much standing or walking you can do. They can not fire you for not being able do it. They should be able ti make a reasonable accomadation for you. As long as you can still do the job they are asking.