Toure complained that he was subjected to monkey chants during Manchester City's Champions League win at CSKA Moscow, and UEFA subsequently hit the Russian club with a partial stadium closure for their European fixture against Bayern Munich later this month.
Toure was so upset by the abuse he received that he suggested black players could boycott the 2018 World Cup in Russia if such incidents were not stamped out.
Swansea are the first Barclays Premier League side to play in Russia since Toure's abuse, but goalkeeper Vorm, who was part of the Dutch squad subjected to racism at a pre-Euro 2012 training session in Krakow, hopes the focus will be on events on the pitch not off it come Thursday's Group A encounter.
He said: "The Toure story is something that is getting quite big which is logical but I just hope it doesn't happen here and is something we don't want to happen.
"This is my first time in Russia and I hope for a good experience. If something happens then the officials know what they have to do about it."
Swansea head into the fixture top of the group by a point from Valencia, but nursing wounded pride having lost 1-0 to local rivals Cardiff in the Premier League's first south Wales derby.
Vorm was sent off during the final moments of the painful defeat, but knows Swansea need to bounce back quickly as they aim to book a place in the Europa League's knockout stages.
"Obviously you want to win derby games," said the 30-year-old.
"We will try and take any positives that we can but it is good for us to focus on such a very important game because we really need to make up for the game last weekend.
"We made some small mistakes and it's something we can learn from and now this is a good opportunity for us. You never want to lose a game, especially against Cardiff, but we always play for our fans.
"We are top of the group but we have come here for one thing and that's to win. That's the most important thing and give the fans something to cheer. We are close to winning the group so it's an important game."
But one man who will not be there to aid Swansea's cause is Michu.
The 27-year-old Spaniard has scored 28 goals or the Swans since his bargain move from Rayo Vallecano, but was hurt in defeat at Cardiff.
Laudrup had said at the time that Michu would definitely miss Thursday's clash with Kuban Krasnodar and Sunday's Premier League meeting with Stoke, but was hopeful he would be available again after the international break.
However, at his pre-match conference in Russia, Laudrup suggested the Spain international may be out for longer at a time when he is desperately needed with Swansea lacking a clinical edge in front of goal.
"There are some players not at their best," said Laudrup.
"Michu, our top scorer last season, has been struggling for a few weeks and is not 100 per cent and unfortunately he is out again for maybe three to four weeks."
Such a diagnosis would mean Michu, who has started every Premier League and Europa League fixture so far this term, will not potentially return until the December 4 meeting with Newcastle.
Laudrup was keen to make clear that is a worst-case scenario, but also revealed the player has been affected by a problem with both his knees in recent weeks and has gone to Spain for treatment.
"When I say he has not been at his best, it is because he has been struggling with both his knees for many weeks, but he wanted to play anyway and he is one of our most important players.
"So with this ankle injury hopefully he can get both his knees sorted as well.
"He will be away in Spain for a few days for some injections."
He added: "Three to four weeks was the first medical opinion. But we said Ben Davies would be out for three to four weeks and he is back training with us now (after two weeks). It is always better to do it that way, to say a little more rather than reduce it and say it is three weeks and it ends up being five."