I take it you've already chosen the air HD for scratch in Photoshop's Preferences. If not, you can do that now. The external drive could be used for scratch, but it could also slow things down considerably because it ( Photoshop ) will be grabbing resources from far away. And, if it's a USB external drive, well it's not the best setup. See is re-setting the scratch disk preference will get rid of that pesty warning dialog.
What is the error message that you get? Do you get it at launch of PS or while setting it up in preferences ? Change the scratch disk settings from PS Preferences(Edit->Preferences->Performance) and then check.