I would totally agree with Joe:
If you come in from Saudi Arabia on the coast road you might be able to get further south along the coast road to Mokha and ship to Djibouti from there.
But then there are the pirates who have come a lot further north into the Red Sea now. It is quite a risk and unless you are a hundred per cent sure that you find a captain whom you can perfectly trust not to strike a deal with the pirates you should think twice before going on a Dhow with the bike!
Coming from Oman you might be able to reach the Hadramaut unharmed, but the way further west is basically off limits! The only option would be the coast road to Aden. There is no way to go from Shibam directly to Sana'a. The way from Shibam southward to Mukalla is highly dangerous! On the coast westward the security forces might not let you cross through uncertain territory between Mukalla and Aden, at least not without a police or military escort. And lastly, the road north from Aden to Sana'a is certainly also not without risks.
All in all: I am sure it is not worth all the risk-taking right now!