There is indeed a certain group of fighters that are slow as hell yet still punch hard. Margarito for example. Pavlik I think is also mentionable. (hearns not at all though , he was fast as hell, definately a fast-twitcher imo). The fibres definately has something to do with it, but it's not 100% it though. It's a combination of different factors.
Sit ups of all kinds are a big yes. With weights is also good but be careful. Leg power will come with squats. But I would also strongly recommend the clean and jerk and deadlifts in addition to squats. Go for reps early. To build really explosive power though, I highly recommend plyometric exercises. Plyometrics techniques for arms, legs and body overall can greatly help build EXPLOSIVE power. But again, start slow and stay there for at least 3 months. Then slowly start adding to your workout routine. Give time to your muscles and joints to adopt to the extra demands you will be placing on them. Also, run sprints. I mean full blast, as fast as you can go sprints. Do 4 to 5 1oo yard dashes every other day (days you don't lift weights). The more you sprint, the more your body will adopt to explosive demands. Speed X Mass = Power. If you increase either one without decreasing the other your power will increase.
Yeah I think Kostya would actually do about 1000 polymetric pushups in an hour[yt]90xhaI8TNgA&NR[/yt] Watch the other polys under the video too
Lots of punch power is generated through .. snap (correct timing...) Core rotation... correct mechanics.. (all the movements running in sequence) Power punching comes largely from your ass.. Glutes play a massive part in all powerpunches.. Rear leg muscles push the power from a sturdy base towards your upper body with help of the importance of rotation.. Solid Triceps help a lot too with the extension of the punch from the shoulder..