Simply keep evading. This should make things faster if you're trying to optimize the time in getting surfing/flying Pikachus. So this isn't just drivel, I'll explain.

Assume you only ever decide to evade in Pokewalker battles for these scenarios.
Now, it's very unlikely, but it is possible that your opponent would ever choose to evade too. If this happened, as small of a chance it is, it would cause a causality loop. Thankfully, either Gamefreak knew this and programed accordingly, or at least it will never actually happen.
So an alternative is to attack, right? Well if that were true your opponent would miss and you'd get an attack of opportunity. Ever time. You Would Never Get Hit Ever Again. This cannot happen either.
So the only option is that, if faced with enough 'stare downs' your opponent would run, no matter what. I decided to test this theory and I conclude that yes, after 3 or 4 CONSECUTIVE stare downs, the Pokemon always fled.