I wouldn't lock him up. You're worried about 1 week's mud? Lucky! It's been a quagmire here constantly since last October!!
They tend to be fine with a week or few here & there IME, but long term wet is bad news.
Re the flaring, I'd suggest just keep it well maintained - 4-weekly good trims with a good roll, esp on the outside which is under more pressure should allow the flare to grow out and if not, your farrier could show you how to weild a rasp well enough to do 'brush ups' of that toe in between trims.