For the deaf person (I teach at Gallaudet, the university for deaf people, by the way, and in the US at any rate, "deaf mute" is considered a slur. Deaf people prefer to be called "deaf".), you could try A-Beggin' I Will Go. It's in the DT, but Ewan McColl sings it on Manchester Angel with another verse that's not listed:

Oh I've been deef at .... (couldn't catch the words) /
And I've been blind at shaw /
And many's the right and willing lass /
I've bedded in the straw /
And a-beggin' I will go, and a-beggin' I will go.

Apologies for the part I can't remember -- anyone else know this one?
Apparently the beggar isn't actually deaf, but maybe this is good enough for your purposes.

--Sarah