I'm not sure what you want to achieve, just demonstrate that the transformer can basically work as a mixer (similar to it's possible to talk through a tin can telephone) or want to reach specific performance parameters.
Regarding DC bias, without it you have a symmetrical I/V characteristic (with only odd terms ax + bx³ + cx^5...) and you'll respectively miss some mixer products associated with even characteristic terms, like f1 +/- f2, you only get f1 +/- 2*f2 and 2*f1 +/- f2.