There is no language called "Swiss", as there are four National Languages in Switzerland. These are French, German, Italian and Romansh.
"Welcome" (in the sense of a greeting) is: * Wilkommen (in German)
* Bienvenu (in French) * Benvenuto (in Italian, for one male person), "Benvenuta" (for one female person) and Benvenuti (for several people regardless of gender) * Allegra (Romansh)
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Depends on which region you are from. In Zurich and most of eastern Switzerland, they'd say, Grüetzi miteinand, Wie gohts? In Bern they'd say Grüessech miteinand, wie geits? Less formally, you'd say Hallo zäme or Hoi zäme. In Bern they even use the French a lot of times and say Salut zäme.
The Swiss language is pretty much German so its Guten Morgen. or Morgen for short.