MySQL using swap during conversion to InnoDB
To switch of MySQL engine you could :

1 Make a ALTER TABLE myTable ENGINE=InnoDB

2 Make a mysqldump of your table, then edit the CREATE TABLE statement to replace MyISAM by InnoDB and restore the dump in the new table (i called it myTable_InnoDB):

DROP TABLE IF EXISTS `mytable`;
CREATE TABLE `mytable` (
  `id` int(11) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;


. 

DROP TABLE IF EXISTS `mytable_InnoDB`;
CREATE TABLE `mytable_InnoDB` (
  `id` int(11) DEFAULT NULL
) ENGINE=InnoDB DEFAULT CHARSET=latin1;


Best regards