Secondary Short Stack, Already in The $$ problem

Okay, I don't have a Hand History, so I will replicate the hand as best as possible. I am mainly concerned with this TYPE of situation, rather than this specific hand. Here goes:

PP $11 SNG, Three handed
Blinds 200/400

Button/Chipleader = t6000
sb/Hero= t1500 (before 200 sb post)
bb/Shorty= t500 (100 behind after bb)
Dealt to Hero Kd2d
Button raises to 800,
Hero...?

I am interested in what you guys think of this situation. I had a strong sense to push. The button had a huge chip lead and was trying to shut me out against the short stack, who was effectively all in. While K2 is not a great hand, I thought that it might be strong enough, in combination with the button's hand, to be worth a push. If the button wins the hand, tourney over and i take second anyway. If I win the hand, then I'm guaranteed second and close to even in chips with button. However, I did not want to triple up the shorty, so I reluctantly folded. I feel like I made an error. I am interested in knowing if you think a push would have been correct as a secondary short stack? If K2 suited is not good enough to make this play, what hands do you think are? Is this a situation where it is correct to push any two hoping one of you can eliminate the short stack? If not any two, what hands should I push here?