In a statement published on Monday, the Swiss foreign office said the SHA personnel were despatched to the region on November 12th after Slovenia and Croatia applied to Switzerland for help at the end of October.
Comprising some 700 people, the SHA is a humanitarian aid corps which is available for direct actions and secondments to international organizations.
The Swiss team will aim to share their expertise and help adapt the existing infrastructure in Slovenia and Croatia to the winter conditions.
The most pressing needs identified by the SHA in the region are better winter infrastructure and sanitation facilities, more translators and support services for volunteers.
The SHA is currently working in the Šentilj transit centre on the Austrian-Slovenian border and will extend their activities to Croatia in the coming days, said the statement.
Between 4,000 and 7,000 people are crossing into Croatia and Slovenia every day, fleeing war in Syria, Iraq and elsewhere.
Switzerland has already provided 1.5 million francs to countries including Serbia and Macedonia in response to calls from the UN's refugee agency, UNHCR.
However the country's main efforts regarding the refugee crisis have been in the conflict zone itself, with a total of 203 million francs given to projects in Syria, Lebanon, Jordan and Iraq since March 2011, said the statement.
As for the situation in Switzerland itself, while it is now expecting to exceed the figure of 29,000 refugees initially predicted to arrive here in 2015, the country is still receiving far fewer migrants than the rest of Europe.
According to the UNHCR more than 800,000 people have arrived in Europe during the crisis and 15 million have fled across the Middle East.
The Geneva-based agency has launched a winter crisis appeal to help refugee families facing the cold months ahead.
After mild weather across much of Europe during November, temperatures are set to drop this coming weekend.
On Tuesday the United Nations called on states not to "backtrack" on pledges made to host migrants and refugees, including from Syria, in the wake of the attacks in Paris on Friday, reported agency AFP.
"We are concerned about the reactions from some states to end programmes being put in place, backtracking from commitments made to manage the refugee crisis," said UN refugee agency spokeswoman Melissa Fleming.
"Refugees should not be turned into scapegoats and must not become the secondary victims of these most tragic events," Fleming added, after some EU states indicated they would take a hardline on the migrant crisis following the attacks.