The Romanians were crestfallen to lose 2-1 to hosts and favourites France in the dying moments of the tournament opener on Friday, Dimitri Payet's long-range stunner ending their stout resistance.
Iordanescu's team, which conceded just two goals in qualifying -- the best defensive record in the preliminaries -- were surprisingly enterprising going forward versus France and should pose even more problems to the Swiss, who beat Albania in their opening match, in their next group A encounter.
But Rat's form will surely be a concern. The 35-year-old recently returned from a shoulder injury and struggled to cope with the exuberance and trickery of France's Antoine Griezmann in the first half, while substitute Kingsley Coman's pace was equally troubling to the Rayo Vallecano defender late on.
Shaqiri, with 17 international goals in 54 appearances, boasts similar qualities to both those French attackers, and will fancy testing Rat's possible shortcomings.
Should Iordanescu, in his third stint in charge of the national team, opt to drop Rat, he could select 22-year-old Steliano Filip.
A downbeat Iordanescu had warned after the France defeat that his players were exhausted and it would be difficult to rouse them psychologically to face Switzerland, which suggests he will freshen up his line-up for the Parc des Princes encounter.
Other selection dilemmas include whether to persist with young striker Florin Andone, second-top scorer in Spain's second division this season, or instead start with Denis Alibec, a substitute at Stade de France.
Likewise, speedy winger Adrian Popa may give way to the more experienced Gabriel Torje, but Nicolae Stanciu's place seems assured after his sparkling creative display.
The Swiss, seeking to advance to the knock-out stages of the Euros for the first time, were efficient in defeating debutants Albania 1-0.
Centre back Fabian Schaer's early header proved decisive, although keeper Yann Sommer also made two outstanding saves to preserve their slender lead.
The Swiss line-up is likely to differ little against Romania, with coach Vladimir Petkovic preferring a settled team. Of the 11 players that started against Albania, eight played in at least eight of Switzerland's 10 qualifying matches.
That means Granit Xhaka will attempt to boss proceedings from midfield, Shaqiri will drift in from wide right and Stephan Lichtsteiner and Ricardo Rodriguez will surge forward from full back.
A win over Romania, or perhaps even a point, will all but ensure Switzerland's progress to the next round. Yet defeat could still put their place in jeopardy, with France, who thrashed the Swiss 5-2 at the 2014 World Cup, to come in their final group game.
(Editing by Ian Chadband)
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