Probably the best idea is to take the train. Your walking options would be....watch from the PoC side (vs the Splash Mt side) of the street, then walk over to Main St, past CP and through the Emporium. You could still get stuck though...won't be able to cross the street there if the parade is there.
Or....watch from the Splash Mt side, and walk back along the wooden walkway beside the lake, up past HM and through FantasyLand and out on the left side of the Castle....then walk the sidewalk past the shops and out..since you're on that side of the street, you won't be hindered by the parade if it's passing.
But, all in all? The train is the best idea!!!