As ylermenezes mentioned cooking accounts for less than half a percent of total natural gas. So, no, we don't need to start somewhere. We need to start where it makes a difference.
60% of US electricity is generated from fossil fuels (1). 40% of that is from Natural Gas. 20% from Coal which produces almost twice the carbon as Natural Gas.
And (2) says 60% of that energy is lost in conversion. So, converting from natural gas to electricity would actually increase carbon emissions in many parts of the US.
So, where should we start? I'm not an expert, but just this quick analysis says decreasing the amount of fossil fuels used for US generation would be a much better choice.
1. https://www.eia.gov/tools/faqs/faq.php?id=427 2. https://www.eia.gov/todayinenergy/detail.php?id=44436