The audio has a sort of glottal stop between m' and ainm. Is that correct? Or should it just be pronounced /manim/?
Like what you have.
I actually like the glottal stop that you pointed out, it makes it easier to understand what's being said. It's probably a Munster thing.
And shouldn't shínigh be [hi: ni:] (palatalized) too?
According to teanglann.ie, munster pronounces the gh at the end as /g/