As far as I understand your question, the answer is "no". Consider the Whitehead link.
https://en.wikipedia.org/wiki/Whitehead_link
The two components of the Whitehead link are unknots (thus they are isotopic) but they do not cobound a cylinder.
Thank you for clarifying that you wish to assume that the given link is "split": the components are separated by a two-sphere. In this case, the link is a "split unlink": a distant union of unknots. As Bruno points out, this is an exercise.