I cannot find a birth on line for Emmanuel and the whereabouts of records for Leck pre 1800 are not exactly clear. I did come across the following baptism at Manchester Cathedral on 12 Jun 1796, parents James Hutchinson & Betty but no Christian name for the child. However it looks from other possible baptisms, which may link to them, they may have moved around the county
I did find his death/burial record but the date differs to yours?
Emmanuel Hutchinson Death was registered Jul 1872 - Lunesdale, Lancashire
Emmanuel Hutchinson Age: 76 (1796) Burial Date: 9 Aug 1872 Leck, Lancashire
I also found the Barbados connection, the first entry 1817 the last 1834.
Slave Registers of former British Colonial Dependencies, 1812-1834 on Ancestry.
These show records of slave births, an Emanuel John Cock Hutchinson is noted as a slave owner.
Regards
Colin