I keep a quick detailer in our cars, too, but also carry an IPA solution in a big bottle, because you never know. I recently learned though my own testing that coconut oil, refined or not, works really well at softening up tree sap and bird gunk. It all falls off after your presoak.
I don't think anything will happen to the car in such a short time. Especially when you recently waxed it. The idea of eggs damaging car paint goes back to the days of single stage paint. Before washing it, I would spray it down with a few layers of a softening solution and then gently wash the dried stuff away.
Issue is my job of being a pilot. I'm on a 4 day trip. Now I do have a 5 hour sit back in base tomorrow and I'm hoping that doesn't change and can sneak back home to get it off. But if that does change, won't be able to do anything until Friday.
If you could get your father cleared to access the airport parking, he could take it home and do it for you.
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In the absense of a paper towel, I'd go straight for microfiber to wipe the worst off and then the quick detailer. Microfiber towels are cheap enough these days that I don't think twice about tossing them if they get too nasty(although if they're not too bad just wash them without fabric softener).
Good advice! I believe Bounty makes a line of automotive paper towels that are very thick and don't tear up easily and leave no lint. They're made for cleaning up grease, but I've found they're really good for removing nasty gunk here and there with a little quick detailer.
But as you said, microfiber is dirt cheap nowadays. It's very easy to stock up on them. I recommend buying good towels and ones you aren't worried about ruining. For the latter, I've found the Kirkland Eurow ones to be decent. Though they seem to sell a thicker version in the summer and fall. Regardless, microfiber makes cleaning and drying things fun. Otherwise car detailing sites, Amazon and their related sites, Jet, et al. run sales almost monthly on large bundles of microfibers.
Alternatively, if you're picky like me, you can grab a Metrovac Air Force Master Blaster or similar. Makes drying a car fun.