Szapszalism" is a convoluted form of Karaism invented in the first half of this century by the Sharaya Szapszal. Szapszal was elected to the post of "Chief Hakham" of Crimea, and later became Hakham of the Karaites of Poland. He was a totally secular man who was known for his fascination with horses and weapons. He preached the idea that Karaites accept Muhammad and Jesus as prophets. This was mainly for external consumption, i.e. to make the Karaites appear more palatable to their Christian overlords and get better terms as a favored minority. Szapszal encountered fierce opposition to his heresy.
Recently, some contemporary Karaite documents were translated from Russian into Hebrew in which the Karaites criticize Szapszal and call him "a black figure." They warn that his election (the documents are from 1911, before he was elected) will cause "the complete disbanding of the Karaite nation." This prediction came true, and Eastern European Karaism, devoid of any moral leadership, stood no chance in the face of Soviet anti-religious policies. In fact, Karaism was the FIRST religion to have all its houses of worship shut down by the Soviet Union.
As a curiosity of history, "Szapszalian Karaism", which professes a belief in Jesus and Muhammad as prophets, has made a comeback since the fall of the Soviet Union due to the efforts of Christian Missionaries. A Karaite that recently emigrated from the Ukraine to Israel, reports that there is great resistance to the missionary efforts, although the resistance is penniless. There has even been a prayer book printed under, which includes the "Lordís Prayer" (from the New Testament!) in Tartaric.