The visitors start the match three points behind the Swiss in the battle for second place and a play-off berth from Group C, knowing a win would keep their fate in their own hands but that a defeat would be a massive blow to hopes of reaching Qatar 2022.
Even so, Davis believes home expectation mean it is the Swiss, ranked 15th in the world compared to Northern Ireland’s 47th, who carry the greater burdens.
“For me anyway, the pressure is on the Swiss because it is a game they are expected to win,” Davis said.
“They will be expecting to progress from the group and will have to put themselves in a position to do that.
“But our pressure comes from within our own camp. There’s just a desire to try to put ourselves in a position to qualify at the end of it.”
Davis will earn his 129th cap on Saturday night but will hand over the captain’s armband to Paddy McNair as the Middlesbrough man gets a landmark 50th.
“Paddy just has to go out and concentrate on and play his own game,” Davis added.
“Whenever he does that, he always brings a lot to the team and that’s important.
“It’s great that he’s amassed 50 caps at the age of 26 and he fully deserves the armband for this game.
“He’s been in and around the squad for quite a while and he is a top player, for me, and I know he just wants to kick on again and keep progressing.”
McNair may be a decade younger than Davis, but the Rangers midfielder said it was not McNair’s half century that made him feel old, but rather taking on the likes of Conor Bradley – who was less than 18 months old when Davis made his international debut – in training.
“It’s more the 18 and 19-year olds, who are half your age, running around you and you’re trying to chase after them in training,” he said.
“But it’s great for Paddy and if he continues what he has been doing, he can go on and win as many caps as he wants.”
Bradley was one of the young players to make an impression in last month’s camp, making his competitive debut as a substitute in the goalless draw against Switzerland at Windsor Park, getting the Green and White Army out of their seats with his attitude in chasing down lost causes.
“The last camp was really positive for everybody,” Davis added. “It’s been difficult at times in terms of selection issues and we’ve all seen over the years how important it is to have a settled side.
“When you’re missing your big players it can be very difficult, but the younger lads have handled that really well and really stepped up last month and we know it’s going to have to be the same again.
“As a young player you just want the opportunity to be able to go and show what you can do.
“It’s maybe come a bit earlier than they thought, but when they’ve come in they have stepped up to the plate and shown their qualities.
“They will now be fighting for their place, which can only be a good thing because it brings competition.”