How to unsync without access to the computer

There is no way to "unsync" an iPhone.

In regards to iTunes content, an iPhone can be synced or manually managed with music and videos with an iTunes library on a single computer only, and photos can be transferred from a single computer only. When transferring iTunes content and photos from another computer, all iTunes content and photos transferred from a different computer will be erased from the iPhone first, but your entire iPhone is not wiped. You can sync contacts, calendar events, and Safari bookmarks with the supported applications on multiple computers.

Since you reformatted the hard drive, your computer is detected as a new or different computer.

An exception to this is if you included your iTunes library with your computer's backup before reformatting the hard drive - the iTunes named folder located in your Music folder where all iTunes content is stored.

Did you include your iTunes library with your computer's backup along with all other important data before reformatting the hard drive? If so, how was this done?

If you copied the iTunes named folder and restored if from your computer's backup placing it in the same location with iTunes quit when doing so and you have re-authorized your computer with your iTunes account with iTunes, your iPhone should not be erased of all iTunes content with the first sync. If you backed up your iTunes library in a different way, the worst is your iPhone will be erased of all iTunes content first with the first sync but your selected iTunes content will be re-transferred to your iPhone.

Contacts and calendar events are designed to be synced with a supported application on your computer. If you aren't doing so, contacts and calendar events on your iPhone will not be touched.

Photos in your iPhone's Camera Roll are not included with the iTunes sync process except for being included with your iPhone's backup which is updated by iTunes as the first step during the iTunes sync process.

Photos transferred from your computer to your iPhone are not included with your iPhone's backup. Photos transferred from your computer to your iPhone should remain on your computer or in this case, should have been included with your computer's backup along with all other important data before reformatting your computer's hard drive. If you restored the photos transferred to your iPhone from your computer's backup, these photos will not be lost if they are erased from your iPhone with the first sync - but these photos will not be touched on your iPhone unless you select Sync Photos under the Photos tab for your iPhone sync preferences with iTunes.

Your email account or accounts on your iPhone will not be touched, nor will your iPhone settings.

3rd party apps are stored in a Mobile Applications named folder in your iTunes folder. If you didn't include the iTunes named folder with your computer's backup, all 3rd party apps will be erased from your iPhone with the first sync. With your iPhone connected and without syncing, at the iTunes menu bar go to File and select Transfer Purchases From - the name of your iPhone.