I suppose it would depend on the emissions laws for the particular state.
Not all ECUs store the vin (don't know if the VX does or not) I don't think there is any problem swapping an ECU for another compatible ECU since they do break sometimes... you might even be able to find someone with Isuzu programming equipment who is capable of swapping the vin in the ECU if necessary.
As far as emissions are concerned on a federal level... you're not allowed to remove any of the emissions equipment, and if they need to be replace they must be replaced with OE parts, if OE parts are not availble then they maybe replaced with similarly speced, certified, aftermarket replacements.
It is perfectly legal to swap the engine and transmission out completely HOWEVER the engine must be from the same model year or newer vehicle, it must be an EPA approved motor (that basically means it needs to come from a car originally sold in the USA), and you must preserve all of the original emissions equipment from that motor.
Obviously some states are more forgiving than others, CA is the worst, as everything in the engine bay needs to be CARB approved, so if you do an engine swap your custom headers built to make it fit will cause it to fail ... that doesn't mean you cant do swaps though... I know Hinson Supercars makes a swap kit to put a Chevy LS1 in a Nissan 240sx and they built custom headers and got them CARB approved making the swap 100% legal in CA as long as you use a factory CARB approved LS1 engine with all the original emissions equipment.
I don't see any real issue with swapping just the transmission and computer out, as long as the computer is a "factory replacement" for that motor since depending on how you look at it the ECU is part of the emissions equipment.
I'm in NH and the only form of emissions testing done here is hooking up to the OBDII port and checking for codes, as long as the reading comes back clean you're good to go, they don't even do a sniffer test and pre ODBII cars (1995 and earlier) are completely emissions exempt...
Even if I left the auto computer on there and it threw transmission codes, I believe a good shop with an intelligent tech would realize that the codes he was seeing weren't relevant to the emissions system.... or you could "know someone" I drove a WRX with no emissions equipment for several years and never had a problem getting a sticker... these days I'm trying to stay 100% legal, but at the same time my summer car is a 1995 240sx, and I bought that year specifically so I wouldn't have to worry about OBDII and emissions testing (hey legal is legal).
Most states don't even do emissions though.