I don't think Seth had a death wish, nor do I believe he came to Deadwood to die. He came with his partner Sol to open a hardware business and expected the arrival of his wife and son.

That being said, Seth had an explosive temper and unmatched pride. Seth needed to get his gun and badge back after the fight. Not returning with these wasn't an option. I don't think either Al or Seth wanted any return to violence. Had Al refused and Seth walked in to take 15 bullets to the chest, the entire camp would have fallen apart (or at least there would have been mass bloodshed). Both Seth and Al knew that. That's why Seth can set those terms and frustrate Al.

As to the line he gives Jane and Charlie, he just means secure his gun and badge back on his own. He doesn't want/need their help.

Anyways.