Gun ownership would have had little effect on partisan activity. Thinking otherwise is basically believing the self-serving mythologising of US gun-nuts.
Don't believe me? Well, let's take a look at which countries in the world, other than the US, have relatively lax gun laws at the time and which ended up being occupied: Belgium, Czechoslovakia - neither of them countries known to have high levels of partisan activity during the war.
The basic fact is that gun-ownership, by itself, does not really make partisan warfare any easier. You do not fight a war against organised troops backed by tanks and artillery with hunting rifles, shot-guns, and revolvers - at least not a war that's going to last very long. The occupiers will simply beat down resistance, demand that anyone who has a gun hand it in, and hang anyone who doesn't do so. Unless the occupiers truly don't even bother appealing to the local population (like, e.g., the Germans in Poland) there are always enough collaborators to gather intelligence about partisan movements - people who turn in their neighbours simply to settle old scores and so-forth. The US would be no different.
Partisan warfare is fought with organisation, sabotage, spying, assassination, bombings, IEDs. The biggest advantage a country can have is mountains, forest, and jungle - places where partisans can establish base-areas. Here the US actually has an advantage.