I don't think anything but physical (electromagnetic force, of the contact variety) force would work, since you aren't necessarily working with charged particles. The radiation is a non-issue, since you can eliminate all the dangerous radiation easily. Ensure clean, full fission and you'll have no radioactive waste to deal with even, so the radiation is just normal stellar variety, only less dangerous. The problem with anti-matter is that you need a physical object to propel out the back. With fission, you can have the products be the matter (high-energy matter too). Anti-matter annihilations don't leave matter behind to propel the craft, but you could use it for energy (if it's feasible, might be 0-sum, though it's compact, might be worth it). Remember: rockets propel via force-counterforce reactions. The particles fly out at a really fast, and apply an equal and opposite force on the rocket. It takes a LOT of particles traveling REALLY fast (or rather, accelerating really fast) to accelerate a large ship fast enough to get it out of Earth's atmosphere. Anti-matter=no particles.
EDIT: Anti-matter does not explode, but it does release a TON of energy. If it annihilates in atmosphere, then it will heat the surrounding air much like a fission bomb does.