NuWater Chlorine Feeder and Pucks

I own a NuWater Chlorinator that takes those ridiculously expensive cartridges. After taking the unit apart it appears to be a very basic water-in, cycle thru the chlorine, water-out system (unless I'm missing something). Can I just throw in some Tri chlor pucks into the unit in place of the cartridges (maybe have to put a small screen in so pucks don't break off and clog holes).

Thanks