Can I update my iPhone to ios 6.1 without syncing iTunes?

I recently got my iPhone fixed and I have all the music I love (800 songs) and while my iPhone was broke my iTunes library got deleted. So if I sync I won't have any music on my phone. Is there any way I can update without syncing iTunes? If so how?

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As long as you are in iOS 5 or above, under settings -> general -> software update, you should be able to upgrade to the newest iOS. I hope it helps!

Also, it is best if you have your device charging while the update takes place (just in case it runs out of battery)