The issue of Sharon has nothing to do with the Khazars or Reform conversions. I have heard that he is a descendant of Russian Sabbatuniks. Sabbatuniks are/were a group of Russian who had adopted some Jewish customs and rituals, mainly changed their rest day from Sunday to Saturday. Due to persecutions and lack of regitrars, it is possible that some of their descendants mistakenly believed they were Jewish and assimilated to Jews. But I have no evidence about Sharon, only that someone once mentioned a rumour that it might be his case.