A suggestion. You may not need to filter at all. I've been keeping Betta fish in 2.5 G tanks, without doing water changes and without filters or air stones. I do top up to make up for evaporation.
What makes it work is the heavy load of plants in their tanks. Not just moss, though there is a fair chunk of java moss in each one, but Hygro difformis, which is one of the most efficient users of ammonia, etc., along with Anubias, java fern and a couple of frogbit. I have a utility clamp lamp on each tank, 8 inch round reflector sits right on the rims, with a 6500 K spiral bulb in it. I think they're 11 watts, might only be 9 watts.
These tanks have tested at zero ammonia, zero nitrite and nitrate <10, and the fish seem very happy. I feed mostly live things, but with shrimp, you can feed shrimp foods and just make sure you don't over feed.
The plants all came from established tanks and likely brought BB with them. A bowl with nice plants and no filter will look a lot nicer.. and if you want, you can easily add an airstone, which will circulate the water a bit more. A floating plant or two, even a couple of difformis leaves, will keep the water surface clear of any film that may form. Betta fish, because they make bubble nests, tend to get a film on their water, but the floating plants keep it down to a minimum.
Just a thought.. you sure don't need heat for a bowl like this and shrimp will really enjoy climbing around in the plants. A bit of substrate to hold some roots, and a rock or two, it should look really nice.
Because shrimp do need calcium for their shells, it might be to their benefit to do a partial water change every couple or three weeks, to replenish the minerals in the water. You may also find adding a minimal bit of fertilizer helps the plants do better, because shrimp have such a low bioload compared to fish. I put one drop of Flourish in my Betta tanks, twice a week, because I want the mosses to grow better, and I add 3 drops of Excel 3-4 x a week for the same reason. The excel is optional, but I'd consider some plant feeding, as keeping them healthy is essential to making the no filter system work.