In the case where it could end up with guns in the hands of those people who easily lose temper, I'm not all that sure that an Appeal to consequences is as much of a logical fallacy as it usually is.
Relaxing the laws on guns tends to mean not so much that more criminals will get hold of them (but it will, really, even if many would have got hold of them already there is presumably the class of "opportunist criminal") -- but rather that people who, for whatever reason, lose control will suddenly have a weapon capable of killing at a distance and in an instant. This, for me, is the issue, no? In the US we see that a large proportion of gun-related violence is down to people with, say, mental health issues with suddenly the easy opportunity to go down in a blaze of glory, or domestic incidents when one party or both lost their temper, or even accidents when no-one was trying to kill anyone but someone ended up dead nonetheless. Gun control has done a great deal to stop that, and keep the level of violence down, and I'm thankful that we have such tight laws because of that.
Outside the Olympic shooting team -- which, you'd have thought, ought to be able to obtain a special licence independent of a change in the overall law (and even if not then practising abroad is no great hardship)-- there is practically no-one who has any reason whatsoever to need a handgun. So why do we need any form of blanket lift in the ban? We don't.
And if criminals are getting hold of guns anyway, well, presumably it's not the easiest thing in the world despite that -- so why make it easier?