@JASpup :-
One thing you learn in Puppy, very early on, is NOT to try setting the default browser FROM the browser's own settings page. This never, EVER works in Puppy.....something to do with Puppy's implementation of the xdg protocols, I believe. Instead, you use the 'Default Applications Chooser', under Menu->Setup.
And don't worry if the browser you want doesn't appear in the appropriate drop-down box. Just manually edit the entry, and set the $PATH yourself to the browser's launcher. The other way this can be done - same thing, different method - is to go into /usr/local/bin, open the 'defaultbrowser' entry with Geany, then change the $PATH there, instead.
You almost always need to do this with any of the portables, unless you've linked the launcher into one of your 'bins' and re-named it to one of the 'standard' names.
Mike.