Dividends will be paid in BTC, obviously.
So, your decentralized exchange will need external feed for the BTC/USD exchange rate from a centralized exchange?! Nice. People can find solutions to every problem...
seems to me a decentralized exchange allows for a completely free market where the price is determined by the supply and demand.
Companies that already issue securities in a shitcurrency (Lets say USD, bidu, on Nasdaq) can decide to issue a new one in BTC.
It makes more sense if the company deals in BTC as part of their business, and would probably allow for automated reports over the network eventually as well!
Then it's up to the company if they want to get whatever accreditation to act as an exchange and allow for the transfer of BTC bought shares to shitcurrency assets.
In the case of companies that deal exclusively with cryptos, it's much simpler.
EDIT: Therefore... you don't need to feed the prices to it. "meatspace" is also "greedspace" and the prices will adjust on their own through arbitrage if the companies decide to allow exchanging between USD shares and BTC shares internally.