Heros do not need to wash, but washing can help to get your HP to a more comfortable level. I have a friend on a hero who is trying to wash to 30k hp by 160. He made it seem pretty easy so im assuming that just washing to a comfortable level wouldnt take too much effort either. If you absolutely would rather not have to deal with it, you dont need to wash though. Sorry for not having any exact numbers on the levels that you asked about, I dont have a hero, but I thought a mini-response might help a bit.
If you want to HT reasonably early or be more comfortable at zak (being able to tank 2 hits from the body instead of 1 will greatly reduce the risk of dying in case you lag/pet heal doesn't trigger right away) then you will probably want to wash. Fortunately warriors only lose 4 mp per wash so if you were to level up with 40 int total that's already giving you 1 wash per level. If you start this from level 50 or so by 155 you'll have a pretty comfortable amount of HP. My hero was my first char on Royals so I couldn't really afford to start washing until about level 70, and since then I've only been levelling with 40-50 int. Even with that minimal washing I'm pretty comfortable tanking zak at level 131. To actually answer your question I think with no washing at all you'd have about 13-13.5k HP clean at level 155.
