Should be fairly easily doable (although somewhat involved) - you'd want to clone the TV object you want to use and give it a new object tuning. For instance, if you were using the Genius Wall Mount TV to update, clone the object 0x0000000000002E5F and replace it's XML tuning (0x000000000000903D, object_tvWallHIGH2x1_01) with a NEW tuning (don't override the existing one or it will change all TVs that use that XML), removing any references to other channels from the various sections of the tuning file.
*EDIT* Just realized you mentioned which TV you want to use, helps to read - right? Anyway, that InvisiView wall TV is object 0x0000000000009E8A and the tuning for it is object_tvWallDS2x1_01, 0x00000000000099BB
That may change some of the line numbers mentioned below as well, although the sections mentioned should be close if not the same. *END EDIT*
You'll have to make some judgement calls on what needs to be removed and what needs to stay. I'd suggest changing the XML a bit at a time, testing, and then moving on. For instance - and this is by no means meant to be a definitive list:
Remove the entire (lines 21-117 of the current Nov 15, 2017 XML) reference to the mixer_TV_ChannelSurf interaction.
Remove a lot of the state_triggers information related to other channels, e.g. lines 230-240 (those line numbers are from the original, if you removed the suggested line numbers above these numbers won't match anymore!) Those lines will roll movie credits for a comedy if the TV has both the movieScreen_Values_Credits state (time to roll the credits) and TV_Movies_Comedy_2 state (currently showing comedy #2 movie). There are TON of these references, so you'll have to be very careful.
As long as you're careful, you can remove any unneeded object states from the client_states list, e.g. lines 470-472 which create the TVChannel_comedy state on that object. If you're careful to never let anything try to set that state on the new cloned object, the comedy state should no longer be needed on your custom object.
You'll also want to remove any super affordances (starting at line 1776) that allow Sims to try to change channels and such.
Good luck! It's a pretty big project to get it done right and bug-free, but it would be far from rocket science just, as I stated earlier, somewhat involved.