I would probably never accept a duel to the death, but seeing as that's not specified, I guess it could be to first blood, or something like that. That being said, I'm not skilled in really any sort of fighting, but I think I could manage for a little while with my fists if I had to BS it on the spot out of the 3 if someone just randomly came up to me right now.
Although I did do some silly sword fighting with nerf swords once, and I did find out that I can beat a guy who actually knows how to swordfight if I use a sword with roughly 3 times the mass of theirs and power through them. On the other hand I would've caused some collateral damage if there was anything else in the hallway at the time with my "style" of flailing around a large sword until my opponent is disarmed.
I don't think I'd accept a gun duel in any circumstance. Besides those are basically just a whoever-shots-first-wins type of deal, so there wouldn't be much fun in it even if I won.
If I could pick anything to duel with? hmm... Tabletop RPG characters. I've rolled up some serious fighters. I'd like to see someone just try to defeat Pathor Killmuch, or hell, Hack the guardsmen isn't going down anytime soon.