Walters had a penalty saved by Mark Schwarzer in last Saturday's 1-0 defeat at Fulham and in January he hit the crossbar in a Premier League defeat to Chelsea that also saw him score two own goals.
But Pulis retains faith in the Republic of Ireland international, pointing out he had shown confidence to take the penalties.
"People have asked me that, and people say 'we would get him to take it, or we would get him to take it'," said Pulis.
"That's all fine, but do those players really want to take it when the game is going on?
"Jon picked that ball up (in the Fulham match) and there was no doubt about it, he wanted to take the penalty.
"He missed it, and as I have said before, people do things in life sometimes that are not right, or do not go the way they or you want them to go. But that is life, and you have to get on with it.
"You have to make sure you back the players who are prepared to do it.
"If we get a penalty on Saturday and Jon picks the ball up and wants to take it - and there is nine or 10 others who don't - then let Jon take it."
Stoke will be without suspended centre-back Robert Huth against the Hammers, with either Marc Wilson or Geoff Cameron likely to move across from full-back to partner skipper Ryan Shawcross.
They will have to cope with the aerial threat of Andy Carroll but Pulis is confident whoever gets the nod will be up to the task.
"We have Marc Wilson, who has played centre-half before, and Geoff Cameron, who has played for the United States at that position, so we have got cover there," he added.
"We have got Shawcross there as well, and I don't think it will be determined by that single battle (with Carroll), whichever way you look at it."