First, 10.Bf7+ doesn't look right. Blacks most principled reply is surely 10...Ke7 when white's last move looks like a waste of time. IMO white is in serious trouble, as black is threatening ...Bg4, and both the moves that prevent it (11.h3 and 11.Bh5) run into 11.Bh4 with terrible threats.
10...Kd7 is a blunder: White can take the bishop on f2, when 11...Ng4+ is no longer possible, and 11...Ne4+ 12.Ke1 (threatening Qg4+) is simply losing for black.
10...Kd8 is also a very weak move, after 11.Bc4, or probably 11.Bh5
10...Kf8 is not so bad, but white can probably make some developing move (at last!) with 11.d3.
So, black should be fine here. Too bad that 5.Bxf7+ or even 5.d4!? spoil all the fun for him...
I've recently played a game using what seems to be the Traxler's main line in the Nxf7 variation(1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 Bc5 5.Nxf7 Bxf2+ 6.Kf1 Qe7 7.Nxh8 d5 8.exd5 Nd4 9.d6 Qxd6), and my opponent played 10.Bf7+, which I have not found in the forums.
Here, Black has 4 choices: