BrowserTraySwitch does not seem to work on Windows 10 Home. The captured .btsregfile's seem to change 4 keys only which do not do the job:
Line 63: Association_URLPROTOCOL|HTTP||FirefoxURL|!
Line 94: Association_URLPROTOCOL|https||FirefoxURL|!
Line 185: Association_FILEEXTENSION|.html||FirefoxHTML|!
Line 216: Association_FILEEXTENSION|.htm||FirefoxHTML|!
Most everything else is "||_EMPTY_|!".
Right-clicking any .btsregfile, whether for Firefox, Chrome or Edge, always opens IE.
Windows 10 Home seems to have a security policy that hinders changing the default browser via script, at least via a script not run under admin privilege. When trying to make a browser the default browser at its own settings page this does not work as it used to work. Instead Start > Settings > System > Default apps opens, where one can click the current default browser to select a different one.
Maybe at Windows 10 Pro one can change that security policy through the Group Policy Editor gpedit.msc, but for 10 Home I see no chance.
The next best solution: You can right-click Default apps and choose Pin to Start. Then you can change the browser with 4 clicks, compared to the 2 clicks for BTS up to Windows 7.