are you, your techies or your ISP worried about space?
does it matter what size the index is, if its required for the process?
how have you defined the datetime_rx, what data type is it?
i doubt the tabnle type will make much of a difference, but if you can it may be wirth using MyIsam as the data engine, unless of course you need the relational integrity required, in which case INNODB is the only choice.
as to whether you can ditch the datetime value I don't know, that surely is up to your application needs. Unless you have a very very good reason I wouldn't store a date value in anything other than a date datatype