Note: this is not a situation I am currently facing, but I have faced in the recent past. I apologized afterwards, which helped, but I'd rather learn how to fix the problem before it even occurs. My location is Netherlands, but an answer working for various cultures, mainly western, is preferred.
The scenario
I have a situation I need a quick answer to. This person I don't know personally has the answer. I sent an email to them. This gives the impression that the situation is not urgent and they may wait with responding. Actually, they did, since it has been half an hour and I need this answer within an hour!
Meanwhile, I acquired their phone number. I want to instant message or call them to explain the situation and get the answer I need, although I'm afraid that makes me seem demanding, nagging, harassing or makes them think I consider myself too important. What tactics can I use to defuse their negative feelings towards this situation?