You can read large blobs in pieces. First find out which ones need this treatment:
SELECT id, length(blobcolumn) FROM mytable WHERE length(blobcolumn) > 1000000
and then read chunks with substr:
SELECT substr(blobcolumn, 1, 1000000) FROM mytable WHERE id = 123
SELECT substr(blobcolumn, 1000001, 1000000) FROM mytable WHERE id = 123
...
You could also compile your own copy of SQLite and access either the BLOB stream I/O functions or the normal query functions of the C API with the NDK, but that would be too complex in this case.