Searching both 'Chaim' and 'Drachman' under exact parameters, I found 3 matches, of whom only one was born in the appropriate birthdate range to have signed the album.
I found a few members of the Drachman family that are listed on the record as having lived at Am-Bach 15, 30, but not at Kilin 50, including Chawa Drachman (b. 1930, could either be a twin or a cousin), and Hersz Drachman (b. 1928, not to be confused with Hersz Icek Drachman, who was born in 1928. This Hersz Drachman could have been a brother.)
The rest of the family members were all listed as having lived both at Am-Bach 15, 30, and Kilin 50. These include Chana Basia Drachman (b. 1927, a possible sister), Hersz Icek Drachman (b. 1925, a brother or cousin), Mordechaj Drachman (b. 1940, a brother or cousin), Mojsze Henoch Drachman (b. 1900, an uncle or father), and Ester Malka Drachman (b. 1900, a mother or aunt).
Many members of the Drachman family are listed with death information. Chaim died on April 5, 1943; Mordechaj's note (which could either indicate a move or a deportation) indicates a date (September 12, 1942) which coincides with a deportation to Chelmno; Mojsze Henoch died on July 8, 1943; and Ester Malka died on April 16, 1944, and for all of these the cause of death is unknown.
Chana Basia died on September 10, 1943, of what (according to hospital death records), appears to be pulmonary tuberculosis.