Well as I said, I think you could add a column to info_table
alter table info_table add orig_id int;
update info_table set orig_id = info_table_sid;
update info_table set info_table_sid = 456 where info_table_sid = 456;
huh?
alter table data_table drop reference NOT SQL
alter table data_table make reference to info_table.orig_id NOT SQL
You don't seem to understand the requirement. The data_table integer value must be changed - all you are doing is a convoluted column rename on the table holding the PK half of the relationship.