I'm updating the IDs with new IDs, but I need to retain the same ID for the master record in table A and its dependents in table B.
The chunk bracketed by comments is the part I can't figure out. I need to update all the records in table B that share the same ID with the current record I'm looking at for table A.

DECLARE CURSOR_A CURSOR FOR SELECT * FROM TABLE_A FOR UPDATE

OPEN CURSOR_A FETCH NEXT FROM CURSOR_A

WHILE @@FETCH_STATUS = 0 BEGIN

BEGIN TRANSACTION UPDATE KEYMASTERTABLE SET RUNNING_NUMBER=RUNNING_NUMBER+1 WHERE TRANSACTION_TYPE='TABLE_A_NEXT_ID'

-- FOLLOWING CHUNK IS WRONG!!! UPDATE TABLE_B SET TABLE_B_ID=(SELECT RUNNING_NUMBER FROM KEYMASTERTABLE WHERE TRANSACTION_TYPE='TABLE_A_NEXT_ID') WHERE TABLE_B_ID = (SELECT TABLE_A_ID FROM CURRENT OF CURSOR A) -- END OF BAD CHUNK

UPDATE TABLE_A
SET TABLE_A_ID=(SELECT RUNNING_NUMBER 
FROM KEYMASTERTABLE WHERE TRANSACTION_TYPE='TABLE_A_NEXT_ID') 
WHERE CURRENT OF CURSOR_A

COMMIT FETCH NEXT FROM CURSOR_A END

CLOSE CURSOR_A DEALLOCATE CURSOR_A GO