The issue of the bud wood. Quick answer I don't know. I have never done it that way.
When I get bud wood or send bud wood is usually the 3-4 inches piece, with buds.
When I get them, I have stored them in the refrigerator vegetable drawer in a moist paper towel in a zip lock bag. I had grafted bud wood that has been stored in refrigerator for 6 weeks with success. Please let us know what success do you have with the branch in water method.