I’d be tempted to just short the wires together, eliminate the door switch and just tell everybody not to turn it on without the door closed for at least as long as it takes to receive the replacement, but temporary fixes become permanent fixes way too easily.
We limped along the dishwasher that came with our house for a few years, replacing the soap dispenser and the door seal until it completely stopped working. I don’t remember what finally did it, maybe a motor burned out, but the midrange Kitchenaid model we replaced it with certainly is much more quiet. We usually run dishes at night, then go to bed, so nobody was around when it finished for several days after we installed it. Then we ran a load during the day and it informed us it was finished with a strange, long low beep and it took us longer than it should have to figure out what made that sound.