This is a testy situation I run into a fair amount, but I have as of yet for it to be a problem - I just say no. I even put the mic I announce with on a short cable and plug it into the keyboard so noone can use it but me.

But the part that would really bother me would be the implied threat that if I didn't allow someone to sing that my job/gig would be in jeopardy somehow, either now or in the future. I wouldn't work under those conditions.