Well, there was no Dynasty with anything like a valid claim - unlike the Netherlands, who had been a Republic in name only since quite some time.
And there was no bigger neigbhor who could make his territory just that more contigous by annexing all of it, like Austria with Venice, or Sardinia-Piemont with Genoa.
Big neigbhors that might have a chance to annex Switzerland, at the time of the Congress of Vienna, would only include France and Austria...
France - well, they just lost a war, so they can't get additional territory - and if they would get all of it, they would extend quite a bit east.
Austria - is among the big winners, but by many Swiss seen as the long term historic enemy - pacefying the place might not be that easy. To split it between France and Austria - with a few minor territories going to Sardinia or Baden - might be an option, but still - France getting territory should be out...
To give Switzerland as compensation to some deposed King? - Most Kingdoms were actually restored at the Congress of Vienna, so there isn't that a big supply in real pretetenders - may be - as in 'Decades of Darkness' - have Saxony annexed by Prussia, but make the Saxon King the 'King of the Swiss' - with a royal domain in formerly Prussian Neuchatel....
Likely not that a stable construct either - the Swiss had strongly resisted French attempts to establish a Unified Republic, so that Napoleon had to 'mediate' the Mediation Constitution (a very loose Confederation under French protection). A foreign King impossed at the point of foreign guns, trying to establish a strong central government, will likely meet quite a lot of opposition.
Hence the powers concluded that leaving the Swiss alone and guaranteeing their perpetual neutrality would cause the least problems...