I know that people keeping their shoes on or taking them off inside is a contentious issue on MN but surely workmen should carry them regardless. That way, if someone wants you to take your shoes off but you can't for health and safety purposes then you can put those on. If they don't care, they keep their shoes on.
I don't care which one individuals prefer but I'm very much a shoes off person and we've just got new carpets upstairs so when the workman came in, I asked if he would take his shoes off. He said that he couldn't. I asked if he had overshoes and he said he didn't.
Disaster averted as I had some that I gave him but surely it should be something all should carry with them.