Walking boot for injured foot

I'm leaving Japan in two weeks and have just injured my foot such that I will probably be in a "walking boot" for most of my visit. What is the proper etiquette when I enter a home or hotel/ryoken room?

Just cover it with a fresh sock when entering. Hope you get better soon :)

How about carrying a plastic bag?
When you enter, cover your boot with asking "sorry, my foot is injured" or something.

A plastic bag sounds like a reasonable solution to me, as long as I don't offend anyone.

You can't do so without a word, but no one reject your asking permission, I think.
It may be a good idea if you considered preparing a memo in Japanese to show them.
足を怪我しているので、この補助器具をつけたままで失礼します。室内を汚さないようにビニール袋で包みます or something.
(Because my foot is injured, excuse me for being with this support-boot on. I'll cover it with a plastic bag to keep rooms clean.)

Sorry, double post.
In the hotel, you can enter the room with your shoes on, because of Western-style.
Only in ryokans, traditonal Japanese restaurants, someone's house, temples and shrines.

Thank you, ajapaneseboy, for both the suggestions (we will be staying at a ryoken and visiting one or two families) and the written note.