Your logic is good. The rest is somewhat an exercise in mind reading. By saying "excess" they basically want you to assume that iodide will be the nucleophile.
When you said "OH-", probably H2O would be the nucleophile in that case. But that doesn't relate to your question directly, just a random minor suggestion. Halogenation of an alkene makes an acid by product, so OH- couldn't be involved. It would be too basic to form.
Halohydrin formation (where H2O is the nucleophile) is another example where relative nucleophilicity doesn't seem to matter. Water is the nucleophile, even though the halide is stronger, because it is present in excess.