Of course none of them was shook or scared. Khabib and Conor are guys with a confidence in their own skill that only someone at their level can possess, they've shown and proven that over and over again, it's a stupid thing to even discuss about. That doesn't mean they were comfortable with the situation tonight.
Conor was very busy promoting the fight and his whiskey while also trying to get inside his opponents head, getting visibly frustrated with the fact that it just wasn't the right setting for his antics and that Khabib wasn't anywhere close to acting like Jose Aldo or Eddie Alvarez who bought into the trash talk during press conferences (though I still heavily doubt professionals like that felt any of it during the fights, they just lost because Conor was the better fighter).
Khabib on the other hand looked like he didn't want to be there in the first place, directly stating that he knew what this was going to be about - a self-promotion and insult campaign from his opponent, occasionally showing obvious signs of discontempt when McGregor wouldn't let him speak continuously (btw, it's quite the joke to have Dana standing there between them and "guiding" through the conference when he'll allow one man to hijack the show) and when he made some accusations that Khabib just couldn't let slide without a reaction.
In conclusion, this wans't a win or a glorious night for either of the two, but neither was it one that will have an influence on the fight. Both men knew what they were up for tonight, both men probably even knew it was going to be a shit show under these circumstances. Neither one was happy with this arrangement and they both stated it within the first 5 minutes of the press conference. Tonight's loser were the fans and the UFC because we weren't given what we hoped for - another epic PPV press conference with a pumped up crowd and numerous top contenders saying what they have to say with the huge Khabib vs Conor fight taking center stage.