It's not possible to "patch" the old3DS browser, as there is nothing to patch.
I do mean that in the literal sense. It's so bad because it *lacks* functionality.
The reason it lacks functionality is due to lacking the necessary hardware to include that functionality (well, except for TLSv1.2 support, that's just lazyness on Nintendo's part).
For example, there is no HTML5 video support, as decoding a regular "web video" could be barely done in real time, but if you also had to resize it to fit the screen, that's already way too much processing power.
Other features are not enabled due to not having enough RAM available to the browser. I bet most websites you'd visit would fail to fully load due to running out of RAM.
To be honest, it's actually a miracle that there is a web browser for the old3DS which actually works *at all*.