Wiping first is the answer.
Swab - wipe the top and side frames with a sill cloth or similar, making sure to wipe about 1" of the glass as well. If you keep your sill cloth wrung out, it will remove 99% of the water on the frame and on the glass next to the frame.
Then squeegee. If your technique is right, the squeegee will direct the water towards the centre of the glass and there will be just enough moisture at the edge to allow the blade to slide and remove that last tiny bit of water along with any crap floating in it.
Practice till you've got it right, then you'll never need to detail again.
Cheers,
Ian