"If I woke up in a different body", is an interesting thought experiment that can help us feel empathy for other people.
But, if I woke up in another body, I'd be using the neurology of a differently wired brain that reflected the experiences of growing up in that body. In short, I'd be a different person.
Brains build an internal model of the body from biofeedback. If the body changes, it adapts. So if it stops getting sensory input from your right leg below the knee, it adapts to not having it. The neural networks that used to give you the sensation there will be colonised by other sensory input, which will make it feel as if your missing leg is being touched initially, but eventually your brain learns that that sensation is now coded to somewhere else.
Likewise if you have an artificial limb installed which gives biofeedback, your brain adds it into your mental model of the body. In fact, we do this with objects temporarily, like riding a bike.
The book "Livewired" dives deep into how the brain works and adapts. It was a really fascinating read.
So our brains (and therefore minds) are deeply integrated in with our body experience - not least because it is a part of the body, you can't divorce the two. But even if our bodies change dramatically such as losing a sense like sight or hearing, our brains adapt, other sensory inputs colonise that prime real estate of processing power to understand the world with what we have.
Sometimes we live so much in our thoughts we forget that our thoughts are products of our physical bodies.