I need some quick advice....

[scrub]

Not if you want to keep running in them on a regular basis and not hurt yourself--putting in them in the dryer is really bad for the foam.

If you don't run a lot of miles, it probably won't make a difference. If you do, you should just deal with wet shoes.

They dry out a lot quicker if you stuff them with newspaper or something right after you go running in the rain.

scrub