Try stammering only certain things - say perhaps limiting yourselves to words that begin with a certain letter or sound. Or maybe just stammering a select few (but common) words.
Or have it so that they only stammer the first word in a sentance. Or perhaps when they're in a certain mood - nervous or angry.
Sometimes people unthinkingly finish a stammering person's words for them.
I used to know a girl with a stammer. I didn't even notice it - and because I barely noticed it, she barely stammered in front of me.
Speech impediments often have some sort of pattern to them, just like lots of people speak in a pattern and then it transfers to their writing style, but it always depends on the individual.