My intuition tells me that any two topological embeddings of the closed 2-ball (aka unit disk) into $R^3$ are isotopic in $R^3$. Is this correct? Maybe easy to prove?

It seems like it should be easy because the disk is compact and contractible, but I sill don't know what to do about it. I am working on problems in mathematical origami and I'm hoping to use this fact as a starting point in a much bigger proof.

This is not my area of expertise, so any tips on what to search or how to go about proving (or disproving) this would be helpful. I have searched different ways of wording this question and haven't found anything helpful.

I suspect this may generalize to closed $n$-balls embedded in $R^{n+1}$ or even an $(n+1)$-manifold, but I only need the case $n=2$.