Ther are other filters that you can try and because of the small tank,they wouldn't run too much.Penn Plax makes one called Small wonders I think,that work for smaller tanks.You can buy the Set-up with just the filter,or the deluxe kit that also comes with a pump
There are also tricks that you can do for the filter that you have.On filters that I thought were too strong for my Betta,I added lots of silk plants,or a tall ornament, right where the water fell out of the filter to help block some of the movement..That seemed to break the quick moving speed of the water.
Being that the filter is the main place where Bio-Bugs lay to cycle your tank, removing it would surely remove your cycle.You have the option of using no filter also,but frequent water changes would have to be done weekly to keep the water safe.
Those Betta's sound pretty awesome.I almost bought a Black one myself-actually he was black/white,very cool looking,but I didn't feel comfortable with getting him shipped now.Good luck,and let us know what you end up doing.