While Southgate admitted they have to make "a decision regarding match sharpness and how quickly you can adjust back into that intensity of the cauldron of the tournament", it might also bring a decision about formation.
Shaw at left-back would mean the manager's 4-2-3-1 in the manner he actually wanted to play it, and it could make another difference.
Decisiveness may be all the more important here, since England have largely muddled through a tournament with a lot of clouded thinking to get this far.
Southgate himself played down the relevance of formation, pointing to the flexibility within games and how "you build with a four, you defend with a five". That may have been a further attempt to cloud things for everyone else, especially given the manager's aggravation this week at leaks about the work on a three-man defence. His comments on Shaw and formation create that bit more confusion.
There may be more to that than just "mind games", since Switzerland manager Murat Yakin was much clearer on how important he sees formations after their last-16 win over Italy.
"I knew that if they play four at the back, then we'll destroy them. We knew we'll flatten them. If they play four at the back, then we'll let them run, and that's what happened."
These were unusually forthright words for a manager at a tournament, especially as regards a peer's decisions, but they were in keeping with the emphatic nature of the Swiss win.
His team did indeed destroy Italy. It is also in keeping with the Swiss thinking going into this quarter-final. There has been a growing feeling that they should consider themselves favourites. This is a team in tune, with a lot of burgeoning talent.
However, Switzerland are a team that have never been past this stage of a major tournament, meaning today represents a real threshold match. That is why there has been such a fervour. That's also why none of this is said lightly.
The tournament has already brought huge surprises. Some of them have come from the Swiss themselves. They took the hosts right to the wire in the group, forcing Germany into a stoppage-time Niclas Fullkrug winner that preserved first place.
They followed that performance with that destruction of Italy. It also comes amid a wider evolution, that has seen the Swiss increasingly maximise improving generations of more technical players.
Manuel Akanji can be considered one of the best in his position in the world, given his role at Manchester City. Granit Xhaka has become one of the year's defining midfielders, given his influence at Bayer Leverkusen. That might have brought mirth in the past but it is a serious challenge. Along the same lines, the Swiss knocked France out of the last European Championship before taking Spain to penalties in the quarter-finals. They're close. They fancy this even more.
Southgate can understand why. He was very struck by the nature of Switzerland's last-16 win in England's pre-game analysis.
"Without a doubt Italy struggled. They couldn't get out of their half. They were determined to build short and they turned the ball over a lot."
He said it all fits with the "energy" around Switzerland.
"I can understand why they feel confident. They're playing very well. They've got some good individual players, there's clearly a good spirit. Fans are having a carnival. They're definitely riding that wave of energy and that's going to make them a formidable opponent, so we've got to be fully prepared."
Switzerland certainly will be, if Yakin's comments on Italy were anything to go by. They will have surely seen so much space in England's performances to exploit.
This is where Southgate's decision on line-up is so crucial. He at least has Jude Bellingham to pick from, after the midfielder escaped suspension for the celebration against Slovakia. The talk in the England camp all week has been how that goal can represent a "turning point". Harry Kane echoed those words on the eve of the game, saying he thinks "100 per cent it can be the spark the team needed".
It's just that Italy might have thought the same. They were a similarly ailing big name with questions over formation that enjoyed a revitalising late goal to keep them in the tournament, in Mattia Zaccagni's stoppage-time strike against Croatia. Switzerland then stripped them of such notions with the reality of the football. This maybe points to the concern with England's extra-time display after Kane's own match-winner against Slovakia. They reverted.
It is entirely possible this performance just goes back to the same inertia. Italy don't have England's talent, though. They didn't have that same momentum either, given that Southgate's side have now reached as late a stage as the quarter-final. The anticipation that comes from being that close to the glory can't be dismissed, or underestimated, given that Southgate is the first ever European manager to reach this stage for a fourth major tournament.
It happens to be the occasion of his 100th game, too. Southgate himself insisted he would reflect on that another time. For this, he is only considering all the many decisions for the game itself.
One is who plays on the left. Will it be Bukayo Saka, Kieran Trippier or Luke Shaw? Will that pick be at left-back or left wing-back? Southgate did make an interesting concession when asked why he didn't bring other left-sided defenders.
"Well, I'm not sure who that would have been because the other options also had injury problems.
"And then we wouldn't have found a better left-footer to play than Trippier has played with his right."
England do have to rediscover the art of midfield control, which the formation is just as crucial to. Would Bellingham and Phil Foden both being behind Kane be too much?
Southgate, despite so much talk of landmarks and how "proud" he is of the quarter-final record, knows this isn't yet enough.
"We haven't come here to be in a quarter-final. There is obviously a missing piece we'd love to deliver."
He first might need to make the team fit, to prevent the Swiss taking it apart. The temptation is there. The risk is there. The stage is there.
England v Switzerland, Live RTE2/BBC1, 5.0