I would make the player explain the reasoning and justification behind these stunts, but I can see a reason for both of these switches.
For the first stunt, the character is tough rather than fast. Instead of being able to dodge blows with Athletics, the character knows how to brace oneself for a hit, how to take a punch and keep going. I would allow it, but put the same limitation on it that Tough Stuff has - it only applies versus 'blunt' damage. Unless you're supernaturally tough, you can't just endure a bullet or a stab wound.
Edit: Or use one of Sanctaphrax's suggested stunts. Those are more awesome.
For the second stunt, this is a character whose self-image is determined by their social reputation and confidence. People love a high Presence character, and this character knows it. The character uses that knowledge as a source of strength when taking mental stress. I'd flat out allow this one, with no caveats; just having the stunt says very interesting things about the character.
The character I play in my tabletop game has some very similar stunts to these. "Give Them Pause" allows her to use Presence to defend against physical attacks, but only when the attackers can hear and understand her; obviously, this has to be accompanied by her doing or saying something that could reasonably make her opponent hesitate. "Must Go On" lets her use her Conviction score to determine her capacity for physical stress; she's able to power through physical pain on willpower alone.