First, when you change the ticker from SNE to SONY, Quicken will ask if you want to copy the old SNE prices to the new ticker. Default is yes which is what you want to do in this case. There is also an option to delete the SNE prices after the copying. I would do that also.
That price history data is the only aspect tied to the ticker. All buys, sells, dividends, and other transactions are tied to the security name. So no transactional continuity is lost. Quicken will be showing purchases prior to 4/21 using the same security name as later purchases.
BUT you seem to keep saying there is a difference in transactions before and after 4/21 which is why I saw this as a two-security issue.