Consider installing a replaceable charcoal filter designed for those.(put it in the basement or behind the frig) The filter and kit cost around $20 some bucks and help improve the taste of the ice.
Consider also soldering in a tee with a ball valve and a soldered in reducer or a tee with a 1/2 by 1/4 compression stop valve to shut the water off. Those needle valves tend to leak after a while and also don't want to shut off. Don't hide a needle valve in the wall.