Ok Akiza's comment is wrong.
Here's what you're telling me: A monster and trap of yours is selected as a target for icarus attack. You play magical dimensionand tribute the target of icarus attack.
The answer is no he cannot choose another. Since he declared 2 targets on the field, if one or both of them are removed because of a chained card, the effect on them disappers. In this case, your trap is still destroyed, but the monster that you tributed and the new monster you summoned are safe from icarus attack.
Source: yugioh ruling page