Welcome to FT
Aurora_82
I think it's just safer to get another one. "washed" passport might raise a few red flags and while you could be OK for the most part (as evidenced by your few trips), there is always a slight chance you may run in to trouble.
I think the urgent service's requirement is usually an itiniary and a general explanation so you should be able to hopefully get it before you leave.
Might I also suggest packing a zip lock bag and leave your passport in there while travelling? It keeps it dry and also nice and clean.
Good luck