As recorded in Baidu, this unique pronunciation of “和” as "hàn" actually originates from the Old Beijing dialect. Extracted from the blog article titled 台湾人为嘛把“和”读作hàn?, it says the following:
In short, a Mandarin Promotion Council was formally established in Taiwan after the end of WWII to restore the literacy level of the Chinese Language. Mr Ji, an old-timer from Beijing, was enlisted to do a daily national broadcast to demonstrate the standard pronunciation of Mandarin through a series of dialogue and reading sessions. The teachers learned as they listened and help spread their knowledge to the students. Mr Ji was widely regarded as a Mandarin guru at that time and he is still a familiar household name for many of the older Taiwanese today.