If you could find a compatible car with steering wheel controls and use the internal parts that would be the best way to do this. Otherwise do you need the remote to be IN the steering wheel? You could always mount it in a panel bolted to the steering wheel column and not need to mess with the internals of your wheel.
Baring either of those you could also use a multi channel remote if you can fit everything inside your steering wheel. (Does your car have an air bag in that year? I hope you are not disabling the air bag? )
A multi channel remote would have a bunch of inputs that you could then send to the receiver to decode. You can use something such as a Aduino Nano as a transmitter and another as a receiver and do whatever you want with them. These should be very small and have the ability to have as many outputs/inputs as you want and you could have a wireless or IR transmitter to do your work. They are easy to program and very flexible. In this type of setup you really only need to close contacts so it should be easy.
Something like this depending on your room: