It should be fine with the filter on just one side then, if you notice the water getting scummy on the other side then you might want to add in an airstone just to break it up. It's not harmful, just looks kinda ugly. So long as the water is circulating through the tank it's fine, which any decent filter shouldn't have a problem with. Do add a sponge onto the intake if you get shrimp, I'm pretty sure they can get sucked up if it's not covered!
Once your girls are on their own they'll probably become more territorial, since their side will be their safe space- and bettas tend to become more territorial the older they get. So even if they're fine now, they might not be in the future if they accidentally get into each other's side. I didn't have any trouble with the dividers I made and siliconed into place, the temporary ones I made weren't the right size so they were more finicky. If you feel more comfortable with the store-bought ones then go for it.
As far as I know the shrimp will either get eaten, or won't find enough food and so any young won't survive long anyway. I don't think I've heard of shrimps overrunning a tank but I could be wrong. Of course your bettas might decide to snack on the adults too, but a lot of people have had good luck. I've never had any shrimp of my own, so someone else might be of more help.