The answer is that both solutions are easy to implement,
if you're properly prepared. And judging from the bikes you have listed in your profile I'd guess you're pretty handy in the garage.
If you're good at electrical things, then changing CDIs would be easy. But you have to be able to accurately read wiring diagrams because the pin placement in the CDI multi-pin connector plug is slightly different between the '91 model and the '93 model.
Did your replacement '93 engine come with its timing disk pickup wiring and connector installed? If the new engine came with its original timing disk pickup wiring in place and you decide to replace the timing disk with a '91-'92 disk you'll have to change the pin-out of the connector to the bike's wiring harness.
If you're good at doing basic wrench-turning things, then the timing disc change would be easy. But you have to have the basic know-how and some patience and the right tools to do the work. I've pulled the timing disc off of my B4 twice or maybe even three times. If you apply heat to the timing disc retaining bolt it will come out pretty easily. Then, if you apply heat to the timing disc the "puller" will be able to pop it off of the crankshaft relatively easily.
If you go with the "replacing the CDI box" option you'll end up with a normal '93 engine. The '93 model engine was slightly de-tuned to 53 horsepower. The '91 engine was a 59 horsepower engine (the '91 has more aggressive camshaft profiles, from the GSX-R400).
Over the years of GSF-400 production Suzuki played confusing game of mix-n-match with specifications with the various GSF-400 models, in Europe there were country-to-country differences. Some European country-specific models got the aggressive camshaft setup while others did not. Some got the BST33SS carbs while others got BST32SS carbs. And in the U.S. there was even a California-specific model that was so horribly de-tuned for California emissions restrictions Suzuki refused to talk about what horsepower it actually produced (you definitely
do not want to put a California-specific CDI on your B4).
Here's a link to an old forum thread that shows the differences between the '91-'92 timing disk and the '93 timing disk. You can see the different tooth arrangement. You can also see that the timing of the spark is slightly "retarded" on the lower powered '93 engine (rated at 53 horsepower instead of 59 horsepower).
viewtopic.php?f=53&t=51944&p=371660#p371660
If you keep your Dad's bike's original CDI and swap out the timing disc you'll end up with a bit of a strange cross-breed of the B4. The '93 engine was a more relaxed, less stressed version with only 53 horsepower. The '93 engine has less valve lift and less timing advance designed into the timing disc (as a result of the de-tuned nature of the '93 engine Suzuki deleted a spacer under the intake valve springs and opened up the valve clearance specifications a bit). So your '91 CDI would be commanding a bit more timing advance on the '93 engine's less aggressive camshaft action. I guess it might produce a bit more horsepower than a standard '93 engine.