long term, yes, but in the few years after the gun ban, the graph goes steeply up, so I don't know how you can draw the conclusion that banning guns had the consequence of reducing gun crime. And the graph I linked to seems to use the same data yours does, so aparently your data is just as worthless as mine.
It's not irrelevant as a large number of firearms were unlicensed. There were a ton of old service guns lying in peoples attics completely unregistered. It takes time to enforce a law.
There are probably still service guns lying in people's attics; I don't suppose much crime is being done with them.
As far as handguns that were in active use - i.e. the ones relevant to this conversation - they had to be (and were) handed over to police within the year iirc. It was done quickly and efficiently.
The licensing laws are and were very strict. Anybody who had a handgun was required to have a licence for it, for which good character references and criminal record background checks were (and are) required, and they had to renew it every year. They also had to be an active member of a gun club (the only place you were allowed to use a handgun), and that membership was also reviewed every year.
So it's difficult to imagine how banning handguns would have much of an effect on handgun crime in the first place, unless you want to argue that licenced gun owners were committing crime and getting away with it, which I don't.
But still, I'm willing to be convinced with evidence. A graph that doesn't show gun crime increasing after a ban would be a good place to start.