All the cable splitter that you linked to does is split the source of the cable wire so you could plug it into two devices such as hooking up a cable box and a cable modem at the same time. however that will NOT allow you to hook up two devices to one port on your tv. If I were you I would do the following.
You have the cable box properly connected to the cable source coming from outside. So now you need to connect the cable box to the tv. The easiest way if you don't have an HDMI cable or the cable box doesn't work with HDMI would be to take one of the RYW cables like this and that should take the audio and video feed from the cable box and display it on the AV input on your tv.
Now to hook up your antenna just simply screw it in as normal and this will show up under the regular cable or antenna input on the tv. so now instead of screwing and unscrewing wires you just change the input selection on the tv.
I have a Vizio and it would display something like this:
AV input = Cable box; TV input = Antenna