There might be a way! In iTune, instead of backing up your iphone to local hard disk, try backup to iCloud. There is no separate password to iCloud, except maybe the password to your Apple ID. So, after backing up the data to icloud, you can wipe your iPhone clean before restoring your backup from iCloud.
However, there is a maximum storage of 5GB on iCloud, unless you pay to purchase more space. Good thing is that there are different ways to get around this restriction:
1. Don't select backup your photos, videos to iCloud. Sync your iPhone and copy your stuff to iPhoto.
2. Don't select backup your music to iCloud. Sync them to your iTunes.
3. Go through the list of apps under iCloud storage management (you can do that under iCloud in your iphone). Turn off backup to icloud for those apps that you do not need, especially those large ones. Of course, leave those essential ones such as whatsapp and iBook turned on.
For me, I have reduced the storage to less than 1 GB.
The above should work, including the case when you choose your backup password, you have not click to select storing the password to the keychain access utility. This is actually my case when I first input the password more than a year ago.
I haven't try this yet as I am still waiting for my new iPhone 5. If you find this works, please share.