I think if you have the time to do it a little more often then do it, but if levels are staying safe you may be ok. I would just keep an eye on the little guy and see if he seems comfortable or not. A small air pump doesnt cost much, if i were you i'd look into getting one. I have 2 betta tanks, and when i started out with them I didnt have filters and had silk plants and toys for my 2 boys, but the water would look cloudy within a day or two, and they're not small tanks either, 3.5 gallons each, so what i did was get two little bubbler filters and ran a splitter to my air pump and fitted a little filter in each tank. The difference was dramatic and the water is never cloudy now. Also if your interested, you can buy some java moss for your guy, its a very hardy plant that you can float in the tank or tie to a rock, or toy/tunnel thats already in the tank. Java moss cleans the water and absorbs alot of stuff that stresses the fish. It doesnt need a lot of light or any special care, it doesnt need gravel either, but if you do have gravel you can wedge it into the gravel and make a bed for your betta. I bought 3 bundles of java moss and added one to my community tank thats fairly well stocked with plants and then took a plastic party cup (clear) and filled it half way with gravel from my community tank, i made a big java moss bush and planted it into the gravel that was in the cup. On top of pulling nutrients out of the water it adds oxygen and my bettas sleep on it every night since its literally like a moss pillow. The plant looks great and grows fairly fast once established, so you'll have a lot more in just a few months and will survive fine with minimal light, my betta's are near my bedroom window and the moss does great with just the blinds open during the day(its an east facing window so it doesnt get intense afternoon sunlight, mostly indirect morning sun and then a decent brightness the rest of the day). I've actually seen bubbles coming off the plant during the day and after seeing how much my boys like that stuff I'll never be without some. Oh and i paid just 2 bucks for a palm sized bunch.
