But it was the edge of the bath that broke my toe.
Ouch. I presume you are certain it is broken rather than the ligaments being strained. If broken you don't want it to set in the wrong position.
Many decades ago I slipped on a step and my foot slammed down onto the step beneath. I howled with pain. The next day there was soreness and bruising, so to spread the load and avoid moving the bruised parts, I wore hiking boots with a solifd wooden sole, and continued as normal.
A week later the bruising was disappearing, but the minor pain wasn't, so I decided to go to the hospital A&E. That was in the middle of nowhere, I didn't have a car, so I push cycled the 5 miles there.
It turned out I had a 1 inch spiral fracture in my fifth metatarsal. Treatment: since the boots were as good as a cast, continue wearing the boots and cycle home
Perfectly satisfactory.
While still booted up, I went to a job interview in a suit and boots. I expected them to ask me the reason for the non-standard dress sense, but they didn't. So I finally told them, they said they were wondering why, and offered me a job. I really enjoyed working at that fun zany place, and learned a lot
The other time I wore suit and boots was to go to Palo Alto on business. That was in the wake of PanAm 103, so there was enhanced security. The staff relaxed after I told them my ordinary shoes were in my case, and I preferred that they were lost rather than my walking boots