I probably wouldn't choose to run the day or two after a half marathon, and depending what the obstacles were I'd probably need a couple rest days after that as well. I usually give a two day rest after a race or intensive/long session of exercise.
I'd look at them as good cross training and not worry about it a bit. It might set your 'weeks' back a couple days but there is certainly no harm in that.
I am not an expert but I would say the walking will not impact on your week 1, 2, 3 or 4. However depending on the type of obstacles you may just want to have a day rest after this race. Good on you for getting into it.
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