As independent as Vatican City -
We could (potentially) add Liechtenstein to the list, although its "independence" from Austria at the end of WW1 may make it ineligible under your criteria. But...Austria didn't technically exist as a country then either. Liechtenstein definitely pre-dates your 1900 date as a principality of the Holy Roman Empire (indeed, the only remaining one today)...but was part of the German Confederation and later the Austro-Hungarian Empire.