The reference to a "current residence address" is actually to a voter's "voting residence address," which is their last U.S. residence address before moving overseas. That is the address that dictates in which state and voting district an overseas American will vote.
Your local election official in the United States must have an exact address or a precise description of where you last resided in the U.S. in order to determine your voting jurisdiction office, and send you the correct absentee ballot with the races and candidates for which you are eligible to vote.
If you are concerned about signing correctly, please contact your local election official in the U.S. and request clarification and confirmation that you can sign the statement regarding your "current residence address." You can look up your local election official's contact information in the Election Official Directory.