If the guns are illegal, they aren't as easy to get. They aren't in everyone's home. If you break in somewhere to steal a gun, you'll not get a handgun. You know, because most folks aren't willing to hold onto an illegal gun. You aren't going to go to a gun show and buy an illegal gun because those folks don't want the shows shut down.

Which does mean that you'll have to go to the black market. The thing about the black market: If something is harder to come by, you'll be charged more. Same if the penalty is higher. You could see this in the drug market: LSD was generally more expensive than weed. (Still probably is, but I really don't know how pot legalisation has affected black market prices).

If guns are harder to get, there is less chance that a mass shooter will be able to get one. Could it mean that they use other means?

Sure they could. But realistically, those options don't always have the same effect. You could build a bomb, maybe. If you can get the supplies and knowledge to do it. Most options available to the average person, though, aren't going to be as deadly as guns and in general, won't kill so many people in such a short span of time and so many simply aren't as lethal.

In this, it is much like suicides. When gun laws are more strict, fewer people choose guns for a suicide. They choose different methods, though, and most of these are less lethal - which overall means that death by suicide goes down.

For a decent comparison, check Australia, which used to have a similar gun culture.