terms can get confusing...
Kalk reactor (not to be confused with Kalkreactor, a specific brand of Ca reactor), is a kalk water or limewater reactor. This simply mixes top off water with kalk powder and stirs it a few times a day so that it stays saturated. The mixed kalk water is then dripped into the system water, usually with a perastaltic pump either on a timer or controlled by a liquid level switch.
Calcium reactors use the Co2 tank. Ca reactors use co2 to drop the PH in the reactor which is filled with calcerous material. The lowered PH allows the reactor media ( calcerous material) to dissolve liberating Ca, Alk, and trace elements. Tank water is slowly passed though the Ca reactor and then back into the system.
I can't picture how to make a skimmer into a kalk reactor but it's probablly possible. If your going to try, some tips;
-The reactor should be sealed (air will react with the Kalk solution and cause precipitation)
-The water needs to be stirred at least once a day
-A pump can be used to stir it but it should be set up so that the paste that settles on the bottom won't be sucked directly into the pump intake
-The output has a very high PH so it must be added to the system slowly.
-It might be a lot easier to buy or build a kalk reactor than to try to convert a skimmer (again, I can't picture it)