Can you swap a '97 Prelude H22a with a '93 Prelude H22a?

Provided the '97 Prelude is a base model, then yes it is possible to swap in an H22a variant. The Prelude Type SH motor is different as the ATTS unit is connected to the motor. So, the only compatible H22a motors would be one from another Type SH, or the JDM Honda Prelude Type S motor.