Before you try the clean install... have you verified that your microphone is selected as the default device in the Recording tab of Windows' Sound settings?

At any rate, every setting you've changed (sans video settings) will be stored in your config.cfg file. That should be located at <Steam Install Dir>\userdata\<Account ID>\730\local\cfg\. The Steam Install Dir is likely C:\Program Files (x86)\Steam\ unless you've changed it. If you've got multiple account ID folders and aren't sure which is yours, you can go here and look at the value after "partner=" in your Trade Offer URL.

However, assuming you don't have any configs left in the deprecated location (e.g. the cfg subfolder inside the CS:GO folder), you won't have to restore that file after reinstalling CS:GO - the installation process will leave it untouched.