302 redirection is fine. About Google Analytics, are you manually inserting the tracking code, or are you using some sort of plugin?
I am pretty sure you are already familiar with the method, if not refer to: How do I manually track clicks on outbound links? – Analytics Help
Google even has a link builder you can find here: Tool: URL Builder – Analytics Help and you should try it out as well.
If nothing works there’s an alternative method with goals but it’s a bit more complicated.
Regards