I don't really buy that it's Walter but I think it would be extremely interesting if it is.
I suspect David has a higher clearance than most considering he was like a son to Weyland. Is that why he uses his own security code to gain access to the colonists? He probably accessed Walter's codes while aboard the Covenant, also.
Also, if it was Walter, why would he speak like David and use all his idiosyncrasies when no one is around? Why would he select Valhalla when choosing music; something which David shows a preference for at the beginning of the film?