In an S-10, the door chime isn't generated by the factory radio (and the air bags aren't affected by removing the radio in any GM vehicle--imagine the lawsuits!). If you have the oversized double-DIN GM radio, use Metra's 70-2003 harness. Check to see if there's a wire in the factory plug that lines up with the red wire in the Metra harness. If there is, then you can just wire up the harness as usual; it should work fine. If there's no accessory wire in the factory plug, then you'll have to connect the red wire to a different key-switched power source. You should be able to find one in the fuse box pretty easily.
A few of the later S-10 models used the data bus system to control the radio power, but none of them ever used the radio to generate the vehicle warning chimes. You can remove the stock radio and it won't affect any other vehicle systems.
If your factory radio is a Bose model, you'll probably need a premium sound adapter to make the after-market deck work with your factory amp and speakers.
