I'm thinking both banjos may have been Paramount, couldn't really tell from the video. Ozzie's banjo, a tenor, obviously tuned like a baritone uke (Nick Reynolds style).
Mr. Botkin's banjo is a plectrum.
I play rythym guitar with banjo players of that style every Tuesday night, as well as occasionally in Assisted Living homes etc.
And I agree, Ricky's Mom sings quite "Swell".....