Two options as you rightly say. You can bypass it, just simply join the pipes together as far back as you can, a bit of copper pipe works well to join them. If you bypass also take out the fuse for the webasto to stop it powering up (however it will detect no coolant and just switch back off).
Personally, I'd try to keep it running as it makes a huge difference in colder weather. Again replace it with copper pipe where it's gone rotten and just cut that piece out and join. Not too bad a job, but it's been a long time since I've owned one and done this job so no photos unfortunately.