If you could find a miniature nice filter that you like, go for it. I have a Finnex PX-360 baffled on my 7.5g for my Betta. He was in a 1 1/2 Gallon jar for 2 weeks before due to purchasing options around my city; he's extremely happy in the tank, and I think he enjoys the filtration. It MAY be a bit too much for him, especially HMDT but I see him having no problems swimming, hell he has a harder time turning around against the glass / plants than swimming. From what I can tell he enjoys it, I know he loves the tank but he's always hanging around by the intake / spray bar when he comes up from the plants.
I'd say give it a try, see how your Betta likes it. They are all different, but I assume at least a bubble thing he would enjoy, and would provide minor current for him.