Ok, so the picture above is how I understand that the selector switch works. You have to press a button and it will allow a certain AV cable to send a signal to the TV, blocking out the others.
You don't want this, right? Because of the hassle of having to get up and change your selection every time you want to change the AV input. Is that right?
So now in this picture it shows that if you remove the selection process (ie, the switch) and solder/tape all the wires onto the set that goes to the TV then you no longer have to use the selection box to change between AV channels. The box should then act as an AV "hub". Similar to a USB hub that you can buy for computers.
There are a few problems with this method though. You would probably have to have all other appliances turned OFF while you are using one that is connected this way. Otherwise you will get interference from the others, causing bad picture and sound quality.
Also, you will have to make sure that you join all the red wires to the red wire that goes into the TV, all the white to the white that goes into the TV and all the yellow to the yellow that goes into the TV. If you don't do this properly the set-up won't work properly.
I think this should work... Can anyone think of any reason why it wouldn't?
Oh and I agree with the person who posted above about the remote. If you do this and then buy one of these "Universal remotes" then you only need one remote for all of your appliances, which is super handy.