If the hotel has a heater or fan or even an open window, hang the clothes near the heater, fan, or open window ... much like you'd do at home. Here in Australia many/most people don't use clothes dryers either.

When I hang my quick drying clothes on the line outside or on the drying rack inside, they are usually dry within a few hours.

If a few articles of clothing are not dry by morning, attach them to the panniers using the straps and cords on the outside of the pannier.

These are a newer version of my panniers. Mine, unfortunately don't have the cords on top which would work great for doing a final dry while cycling. But they do have the cinch straps to hold things on the outside of the pannier, and mine have a mesh pocket which can also be used to dry things. As you look closely at these, you'll be able to see lots of places to tuck and hang stuff ... now check out your panniers and see what options you have.