There is no way around a pump. But the one you have might be okay if you clean it out. If not, a pump with such low volume you should be able to find really cheap. Just make sure to get a real pond pump, not a submersible cellar pump.
How big it should be? Meh, if my math isnt off, the volume of your pond is about 1200 liter. Almost any pond pump will handle that per hour (if you dont have to pump it up much higher), which ought to be more than enough. In fact Id be surprised your current pump doesnt do that.
Question is, where will you pump to? You need 2 things; the water needs to be aerated, by creating a fountain or water fall or something, it doesnt need to be fancy just as long as the water "splashes" and has a chance to interact with air. And it needs to run through some filter media. YOu can do that cheaply, like pumping to the bottom of a rainwater barrel and filling it with old plastic stuff. I used PVC plumbing pipes that I cut in to rings. Works great. Acts as both rough mechanical filter making parts sink, and biological filter as they provide a fair amount of surface for bacteria to grow on. Roughening the surface first is even better.
Then put a pipe at the top where the water flows out and falls in to the pond, and you have a waterfall. If you can create a plant filter, thats even better, but thats less likely to happen in a few weeks I assume.
