Hi JamesPond
You will find information about cleaning hedgehog houses here: https://www.hedgehogstreet.org/cleaning-out-boxes/
As you will see, boiling water is the preferred cleaning material – it will kill any parasite eggs, etc. Hedgehogs are particularly sensitive to chemicals so they are not advisable. I appreciate your point re. the weather and drying, but you will find that most of the water is tipped out and some of the rest evaporates. For the remainder, you will just have to leave the box open for longer – it should dry eventually. Choosing a sunny day should help. But you may need to put it under cover over night.
Alternatively you may like to wait until the weather is a bit warmer – April and October are considered to be the best months for cleaning hog houses.
Good luck. I hope it’s a good hedgehog year where you are.