If it is like one of those small folding camp stools with 3 legs, then no Disney is not going to allow it. They have to allow medical devices per the ADA, but anything else, meant for other functions, they won't allow you to use it.
You will probably have to bite the bullet and either use a wheelchair or rollator or other device like these if you want a seat with you at all times. Just because you bring these with you into the parks, doesn't mean that you have to stay in them all the time. Some people even ride their ECV's to a area. Park it in stroller parking and then hit a few attractions in that area. They then get on their ECV and ride to the next area and do it again if they need to.
You will probably have to bite the bullet and either use a wheelchair or rollator or other device like these if you want a seat with you at all times. Just because you bring these with you into the parks, doesn't mean that you have to stay in them all the time. Some people even ride their ECV's to a area. Park it in stroller parking and then hit a few attractions in that area. They then get on their ECV and ride to the next area and do it again if they need to.