Question about challenges

[arcadiandream]

Hey, didn't really know where else to ask this, so here goes...
When you challenge someone, is there any way to choose what playing style you challenge them with? For instance, if you challenge someone else while playing the diagonal arrow mode, can you make them play in that style, too?
There doesn't seem to be any way to do this, as far as I can tell. I was just wondering if I was missing something, or if it is plain impossible.
Thanks!