Switzerland is currently phasing out from nuclear energy. This represents a real challenge for the country as it represents nearly 35% of its domestic power generation. This phasing-out might further increase the Swiss power import dependency, especially in winter. This winter dependency might become a threat to the security of supply, magnified with the electrification of the Swiss energy system with heat pumps and battery electric vehicles. In this paper, we explore how Combined Heat and Power (CHP) plants fuelled with natural gas or biogas might represent a short-term solution to produce power in winter on the Swiss territory. We analysed the effect of the deployment of this solution on the hourly carbon footprint of the electricity consumed in Switzerland. We used a four-step methodology developed in our previous work but extended the geographical scope of the analysis to Switzerland with its direct neighbours (France, Italy, etc.) and their neighbours (Spain, Danemark, etc.). We run the analysis from the years 2016 to 2020 which allows us to analyse the effect of the decommissioning of the Mühleberg nuclear in December 2019. The results show that the deployment of this solution could lower the GHG footprint of the electricity consumed in Switzerland up to 7.51%. However this effect is fading through time and even increase the electricity footprint for the year 2020. This is mainly due to the fact that the power generation mix of Germany is constantly getting cleaner. We also examined the barriers to the deployment of small CHP units for domestic usage in Switzerland. The results show that the technology is facing many obstacles. As long as there is no clear definition of a strategy regarding CHP technology at federal and cantonal level, a real market penetration seems compromised.