Indeed this is a interesting Question....
But David did manage to find or create... Pens, Paper and also a Grey Jumpsuit ;)
Serious note... i think the reason we see Walter in a Hoody then Hat and David maybe in a Cloak.. is to keep Fassbenders hair under wraps so its not exposed... so its less time having to mess about with color changes via Wigs..
Fassbender calls David Creepy.... so if David can somehow persuade the Crew to let him on board.. and then does away with Walter and uses some Dye on the Ship to then take his place.. This could work..
Then the Crew would wander where the other Robot was..
So nope i think a more Creepy way would be both David and Walter get to the Covenant.... then David in a creepy way like the movie "Single White Female" dyes his Hair to be like Walter..
To in a creepy way seem to idolize Walter, the Brother he thought he never had.... much like how David idolized Peter O'Toole's character in Lawrence of Arabia
It would be perfect set up to have Two look-a likes with no off screen or on screen killing and then mistrust... it would add to the Creepy Vibe of David..
This is how i would have wrote it in.... but then i never was asked lol
My Chest Buster Beater.... would have been Spore infected Pregnant Female... Intimate Love Scene Belly-Burster... but ALAS!