You seem like you know a little about Control Panel and stuff, so I wonder if you know about changing the browser links to open in a different browser in a launcher/game.
I am not too sure about that, but I'd guess a thing like that would require editing the Windows Registry a bit. I am like 80% sure that editing any Maplestory/Nexon related registry keys on your machine breaks ToS though, and if you don't know exactly what you are doing you can easily break a bunch of things, so I'd advise against doing that.
Okay, I did a bit of digging. Registry Editing is quite certainly agains the ToS, and it wouldn't be the solution in this case anyway, so no touchy. At this point there doesn't seem to be a proper solution to this, since it looks like the use of Internet Explorer is hard-coded into the game as changing your default browser doesn't seem to affect anything. Sorry that I couldn't help.