Did Charlie Chaplin fund and produce The Great Dictator alone?

According to article on Vulture, yes.

Wikipedia states,

The film was directed by Chaplin (with his half-brother Wheeler Dryden as assistant director), and written and produced by Chaplin. The film was shot largely at the Charlie Chaplin Studios and other locations around Los Angeles.

From Vulture,

The Great Dictator has rightly been held up as an example of Hollywood not caving to the wishes of foreign tyrants

Plus, Chaplin had already run afoul of the Nazis, who thought (erroneously) that he was Jewish, banned his films, and even called him “a disgusting Jewish acrobat” in one of their publications. When he visited Berlin in 1931 to promote City Lights — well before Hitler’s rise to the chancellorship in 1933 — pro-Nazi media had effectively run him out of town, calling him an “anti-German warmonger” and an “American film-Jew.” Footage of Chaplin’s visit would be used in the notorious Nazi propaganda film, The Eternal Jew. (“It cannot be denied that one part of the German people enthusiastically applaud the foreign Jews who come to Germany — the deadly foes of their race,” the film’s narrator breathlessly warned, over shots of adoring crowds greeting Chaplin.)

The reason for him to do this alone because studios had doubts in the war. as stated in Vulture,

But in 1938, when Chaplin announced that he was setting forth to make The Great Dictator, Hollywood was extremely wary of picking sides in the approaching war. Studios deliberately shied away from commenting on events in Europe and made it a point to take out any material that could be construed as overtly supporting U.S. intervention. Part of it was due to financial relationships they had with the German film market. Part of it was a fear of very vocal isolationists in the U.S. Studio heads also worried that they would themselves become the targets of anti-Semitic attacks if they pressed too hard for war.

In his book, Five Came Back: A Story of Hollywood and the Second World War, Mark Harris describes the tension in Hollywood thus:

Even as most studios maintained a strong financial interest in the German market and continued to do business with Hitler and his deputies, the issue of how to fight Hitler’s rise to power was becoming a subject of discussion, and discomfort, in their boardrooms and executive suites. But in 1938, all of Hollywood’s major moviemaking companies … were adamant on one point: Whatever they thought about the Nazis, they would not allow their feelings, or anyone else’s, about what was happening in Germany to play out onscreen. On rare occasions, a veiled or allusive argument against Fascism or tyranny would make its way into a motion picture, but it was then unthinkable that studios could use their own movies to sway public opinion about Hitler without sparking instant accusations that they were acting as propagandists for foreign – meaning Jewish – interests. Much of Hollywood’s creative class – directors, writers, actors, independent producers – was becoming far more forthright about making its political sympathies known at rallies and in aid organizations, but for the most part, the noise they were making stopped when they passed through the gates and reported for work every morning.

Chaplin, however, had his own studio and could afford to self-finance much of his film. That’s not to say that he wasn’t met with enormous resistance when he initially announced it in 1938. United Artists, the studio he had co-founded, was nervous and worried that the film could not be shown in England, for fear of offending the Germans. Chaplin was fearless.

He himself tells about the problems he had to face in his autobiography:

Half-way through making The Great Dictator I began receiving alarming messages from United Artists. They had been advised by the Hays Office that I would run into censorship trouble. Also the English office was very concerned about an anti-Hitler picture and doubted whether it could be shown in Britain. But I was determined to go ahead, for Hitler must be laughed at…More worrying letters came from the New York office imploring me not to make the film, declaring it would never be shown in England or America. But I was determined to make it, even if I had to hire halls myself to show it…Before I had finished The Dictator England declared war on the Nazis… Then suddenly the holocaust began: the break-through in Belgium, the collapse of the Maginot Line, the stark and ghastly fact of Dunkirk -- and France was occupied. The news was growing gloomier. England was fighting with her back to the wall. Now our New York office was wiring frantically; “Hurry up with your film, everyone is waiting for it.”

There were certain fears at the studios, that made him do all the work himself, which also indicates sometimes he had to face more than just concerns about germany from the studios.