Is a husband's claim of illness to avoid shaking hands with non-mahram women considered a forbidden lie?

Your husband can solve the problem by using tawriya (allusory speech) and ta‘rid (indirect hint); this involves using words that carry different meanings, from which the customers understand something other than what he intends. It is also advisable for the husband to keep suitable da‘wah materials in German, such as brochures, small booklets, or CDs, to provide a general explanation of the religion of Islam, the status of women within it, and related rulings, in an appropriate manner that highlights the virtues of Islam and its consideration for human nature and human interests.