You could design a pulse detonation engine for this. Electrolyze water continuously; detonate it in a pipe every now and then. It's a very simple design that gives you quite a bit of performance for hopping in the asteroid belt. Specific impulse similar to a hydrolox engine, or slightly worse than regular hydrolox engines if operating stoichiometrically, although the detonation mode could compensate for that (detonation rocket engines can potentially get ~10% better Isp performance than "classical" rocket engines). However, you get triple the propellant density (water has ~1000 kg/m³; hydrolox is at around 340 kg/m³). This makes it much better compared to a classical hydrolox vehicle wherever gravity is near zero so that you don't need lift-off thrust.
