First off, all I know about this is divined from the service manual and other member's posts, not hands on experience so take it for what it may or may not be worth.
My initial reaction is assuming that the car still has its original ECU, do you really need to change it? Transmission control is offloaded to a separate module and the service manual suggests that the external pin connections are the same on the auto and manual ECUs. There is a data line between the ECU and the TCM and some other shared connections; but, that data may all be one way (ECU to TCM) Those terminal pins on the manual ECU may still be present, its just that the external harness may not be populated to use those pins. If you disconnect the TCM you may generate diagnostic error code so you might need to leave the TCM connected to the ECU (even if there is no auto gear box) if you want to avoid the CEL indication. You definitely will need to reconfigure clutch and neutral switch connections to the ECU; but, those connection configuration changes all appear to be external to the ECU.
The primary requirement in picking an ECU will be the ability to support drive by wire. I can't remember whether DBW came in 1995 or 1996 which may reduce your range of options. The DBW system did undergo some changes from the early years. I don't know whether this involved hardware or was just firmware tuning. That may or may not present a problem trying to use an earlier ECU with your 2001.
The other things that changed during production is the controls of the evap system and the secondary air system. There was an evolution of the evap system with a final version (I think) in 1999 or 2000. An early ECU is probably not going to play well with a later evap system which will be an issue if you want to try and maintain emissions compliance and not have your car smell like a refinery when it is parked on a hot day. My 2000 Na2 has secondary air injection on start up to fire up the catalytic converters quickly. If your 2001 auto also utilizes secondary air injection an early ECU will lack the controls for that. That may or may not be a problem. There may be some other production changes during production that make mixing an early ECU with a later car a bad idea.
I seem to recall that although the auto and manual ECUs had different part numbers, they were essentially identical. There was an internal resistor or shunt inside the ECU that could be snipped to convert from an auto to a manual ECU . This caused the fuel maps to be switched and perhaps caused the ECU to ignore the data line to the TCM. You don't want to do this because you don't want to switch the fuel maps. However, it suggests that the ECU changeout may not be necessary. Of course, all that is anecdotal because I haven't done it.
There are a number of members who have done the auto to manual conversion on early cars. I believe
@drew has done this and McLargeHuge has a project thread
Hey everyone, I'm Tyler and I’m pretty new to forums in general but wanted somewhere to document my journey with this car, give credit to some long-time members that have already helped me through old forum posts, blogs, FB posts, etc., and hopefully help some current and future owners if they...
www.nsxprime.com
Their experience with converting early Na1 cars may help you suss out the need to change the ECU. As a first step, I would get the service manual for 2001 and the electrical trouble shooting manual and carry out a detailed analysis of the ECU pinouts and the related connections to try and confirm what the differences are. Personally, I would try everything possible to try and retain the original ECU.