Walking up woodcock is not an enviable task, but it can be done providing there are enough of them around - which is always the wildcard with migrating birds.
I hunt east TX with a dog. If I were walking, I would first scout the field edges at daylight and dusk extensively to ensure there were indeed woodcock in the area. You will see/hear them flying in or out of the fields to feed. When you find them that will give you confidence in hunting them. Then I would bust through the thickest cover I could find, areas near drainages, creekbottoms with thick growth, 5-10 year old clearcuts, and field edges at dusk as mentioned above.
It probably won’t be a hunt with a lot of action, which makes it even more of a challenge because the few birds you do get up will probably take you by complete surprise and just getting off a shot will be tough. Every bird will be hard-earned for sure.
But, hey, you will be hunting with your Dad so it’s all good no matter what.