So, I got some liquid soap on my laptop's touchpad and now it's registering swipes or touches when it has been neither swiped nor touched. Can I just wait for it to dry like water or do I have to replace it?
naah - I believe it drowned for good.
If you have some skills in watchmaker work, you may disassemble your laptop and replace the touchpad.
They are available as repair parts.
Try a google, using the exact model number on your laptop.
You may well get results with parts that fit several different models, which you can utilize for new searches and then get more relevant results on price and availability.
Youtube may even have a how to video from other owners with this experience.