If we trace back to late Middle Chinese, 無's onset is 微 (w), while 沒's onset is 明 (m). If we go a little bit further back to early Middle Chinese, we only have the onset 明. In other words, the early Middle Chinese onset 明 （m）has split into two onsets 明（m）and 微（w）in late Middle Chinese. This happened between Tang and Song Dynasties.
However, not all dialects of Chinese have gone through this phonetic transformation. For example, 無 is pronounced as mou4 in 粵方言廣府片 (Guangfu Subdialect of Cantonese), vu2 as literary pronunciation and m2 in oral pronunciation in 吳方言蘇州話 (Suzhou subdialect of Wu).
In Southern Min, most characters with early MC onset 明 have gone through denasalisation to [b] or [mb], but characters with nasalized rhymes and another small amount maintained [m]. Specifically for 無, in Quanzhou Subdialect, the onset is [mb], with a weak leading nasal sound m. In the original version of the song, it sounds like something between [mo] and [bo] to non-native ears. I consulted Taiwan's Southern Min Dictionary, it's pronounced as [bo], as it is case in the very beginning of the speech in in this video from Taiwan. It could be a matter of notation, or a genuine complete denasalisation. I can’t tell.
In your linked video the onset of 無 is pronounced as a clear nasal [m]. But the singer, if not mistaken, is from Northeastern China. She is unlikely able to speak Southern Min.
All that being said, the phonology of Southern Min dialects are very diverse from within. I don't know enough about it to tell if it's indeed a variant of Southen Min or a non-native speaker mimicking the sound.