I never really found an air pump which I considered quiet enough, so often do go with a pump of some sort connected to the sponge. Keep in mind that there is often a lot of confusion about the purpose of the air from air pumps used with undergravel or sponge filters. They are there more for lifting the water around the bubbles and less to get O2 into the water, so when we want to move water through sponge, power actually does move far more water than air bubbles.
I find the main question to be more one of matching the mump in/out fittings and the size to the sponge and pore size. Too much flow/pulling too much debris and we can wind up needing to clean off the sponge way too often. Matching the pore size on the sponge can do lots to change how often they clog but I find the replacement sponges meant for Aquaclear seem to have it down to perfect well enough for me to pay extra for them.
About as simple as one can get is a powerhead fit to the neck of a soda bottle full of filter floss or sponge. Not the nicest appearance but it works pretty good when I hide it behind a rock or wood!
A search for DIY sponge filters might give a jump start for design ideas? Moving the water with a pump is the way I would go. If we look at a canister filter, the only difference is that the media is contained outside, rather than inside the tank.
Perhaps, some the small Sunsun canisters would also be an option? They do cut the clutter inside the tank and are pretty reasonable in price.