If your Mac is stuck on snow leopard, none of the big three browsers will update to the latest version. If you want chrome, I think version 33 is the latest one that works. However, it's lacking the latest security patches.
I would suggest updating os x to the latest version you can run so that you can use a fully patched version of chrome. Provided you are running key applications that are dependent on snow leopard. At which point you have a dilemma.
The Maximum OS is OS X 10.11.6 for your MBA, so Yosemite 10.10.5 should work.
El Capitan is also available from Apple as a free download since you are upgrading from Snow Leopard and can not install Sierra: https://support.apple.com/en-us/HT206886
It may operate a little slower than you like. If that doesn't suit you then you could try Mountain Lion (10.8.5).
Make sure you have a good backup before installing in case it doesn't go well or you don't like it and you want to revert. I would recommend making a clone backup. This is important!