Sikkim in 1900 would qualify as a British protectorate, and as you may notice, protectorates in Asia and Africa are technically under the colors of their relative imperial masters.
As for Andorra, it was historically annexed by France under Napoleon, so there's no reason for it to be independent here, even if I was inclined to include mini-states. After doing some quick research, if there is any tiny nation that should exist in this timeline it is San Marino. It was supported by Napoleon, and the coalitions, and was kept out of the hands of the Pope and Italy. Liechenstien and Luxembourg were not so lucky with the former going to the Confederation of the Rhine and the latter to France.
Of course, we can only speculate as to mighty Sealand, which won't exist for another fifty years.