Have you tried
The sledgehammer approach would be
No more itunes, but no more ANY windows programs that you've installed with wine
(be careful when running that command though)
Uninstalling wine won't uninstall any of your windows programs. All it does is uninstall wine's binaries and libs from the system. Everything that you install with wine by default goes somewhere in your home directory - usually in a folder called '.wine'. Think of it sort of as your "wine hard drive".
If you don't want to delete your wine directory, well...I'm afraid I can't help you, since I've never tried installing iTunes under linux.
Another option to consider if wine ends up not working is creating a virtual machine and putting a windows installation in it, and installing iTunes there.