No one nation has a single influence (for example, the Earth Kingdom has several Korean influences such as some of their [url=https://vignette.wikia.nocookie.net/avatar/images/8/86/Song%27s_mother.png/revision/latest/top-crop/width/360/height/360?cb=20140128110440]fashion designs[/url]). That said, I'd argue Air benders are more Tibetan than shaolin, particularly since shaolin isn't a people or culture but rather a form of kung fu. In fact, fire bending forms are based on shaolin. Air bending is based on baguazhang. The Fire Nation has more Chinese influence than Japanese, particularly in their dress and architecture. Things like the significance of tea are found in both cultures. The only thing that really "screams" Japanese is what they have in common with WWII-era Japan: industrialization and imperialism. Fun fact, the fire nation itself (the geography) is based off Iceland.

Funny how China now is literally Lake Laogai

Meh, That's what they're called. Says they were wanderers by definition but had four air temples