Q: 60W Magsafe for new Macbook Air 13"?

You can use it.

Section: General information

“Power adapters for Apple notebooks are available in 45W, 60W, and 85W varieties. You should use the appropriate wattage power adapter for your Apple notebook. You can use a higher wattage adapter without issue, but doing this won't make your computer charge faster or operate any differently. Lower wattage adapters will not provide enough power.”

https://support.apple.com/en-us/HT201700

Yes you can use it, but is there a reason for not using the charger that came with the new Air?  If you are carrying both the old and new machines and want to save room, not a problem.  But the higher power will not change the charging rate.

Do the same thing with my iPad and iPhone, just take the iPad charger and use that for both.  Too bad I can' tune the MBP charger for all devices