Transmission swap

The computer should fit, but I am not 100% it will work as your wiring harness will more than likely not have all the wiring necessary for the swap.
Things such as;
speed sensors Electronic load detectors
Redline shift points

These all need different sensors and to be wired to the ECU properly.

I have seen auto to manual swaps done and they are generally tough. So, It can be done, it just may be a more time consuming and expensive project.

You might also need some mechanical parts as well;
A transmission mount to work with the cross member.
A pedal set form an automatic RX7.

For some of the best information on the details of this kind of project, (being it is custom), try finding a Mazda RX7 enthusiast forum. That is a popular, and a very nice ride too, so it should not be hard to find a forum and join it and start looking for answers and asking questions.

This is one of those jobs that is hard to say what you will need to make it work. You can make anything work. It just comes down to, is it worth it.
I know some people in the Honda/Acura community that might have good advice for you as they can lead you to shops that do Mazda swaps. I will look them up and give you there contact information if you want it.
I will watch for your reply.

I don't hacwe many Mazda contacts but try Steve at HMotors. Com. He can get anything and ut us high quality as he has people in japan buying itfor him.
Try getting on a Madza enthuisiast forum as they usually have a for sale section and you can get tips specific for custom stuff from people who have done it.