Does a designated harvester or hunter companion need to have a Washington license to harvest for or assist a disabled person in Washington?

No. According to WAC 232-12-828(8), a designated hunter companion must have a valid hunting license from Washington or another state.
The hunter companion or designated harvester must have their licenses with them. And the disabled person who is being assisted must have the appropriate Washington licenses and tags for the activity, plus a designated hunter companion card or disabled harvester identification card for the person harvesting for or assisting him/her.